/* Copyright 2002-2022 CS GROUP
    * Licensed to CS GROUP (CS) under one or more
    * contributor license agreements.  See the NOTICE file distributed with
    * this work for additional information regarding copyright ownership.
    * CS licenses this file to You under the Apache License, Version 2.0
    * (the "License"); you may not use this file except in compliance with
    * the License.  You may obtain a copy of the License at
    *
    *   http://www.apache.org/licenses/LICENSE-2.0
   *
   * Unless required by applicable law or agreed to in writing, software
   * distributed under the License is distributed on an "AS IS" BASIS,
   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   * See the License for the specific language governing permissions and
   * limitations under the License.
   */
  package org.orekit.propagation;
  
  import java.io.Serializable;
  import java.util.ArrayList;
  import java.util.HashMap;
  import java.util.List;
  import java.util.Map;
  import java.util.stream.Stream;
  
  import org.hipparchus.analysis.interpolation.HermiteInterpolator;
  import org.hipparchus.exception.LocalizedCoreFormats;
  import org.hipparchus.exception.MathIllegalStateException;
  import org.hipparchus.geometry.euclidean.threed.Rotation;
  import org.hipparchus.geometry.euclidean.threed.Vector3D;
  import org.hipparchus.util.FastMath;
  import org.orekit.attitudes.Attitude;
  import org.orekit.attitudes.LofOffset;
  import org.orekit.errors.OrekitException;
  import org.orekit.errors.OrekitIllegalArgumentException;
  import org.orekit.errors.OrekitIllegalStateException;
  import org.orekit.errors.OrekitMessages;
  import org.orekit.frames.Frame;
  import org.orekit.frames.LOFType;
  import org.orekit.frames.Transform;
  import org.orekit.orbits.Orbit;
  import org.orekit.time.AbsoluteDate;
  import org.orekit.time.TimeInterpolable;
  import org.orekit.time.TimeShiftable;
  import org.orekit.time.TimeStamped;
  import org.orekit.utils.AbsolutePVCoordinates;
  import org.orekit.utils.DoubleArrayDictionary;
  import org.orekit.utils.TimeStampedAngularCoordinates;
  import org.orekit.utils.TimeStampedPVCoordinates;
  
  /** This class is the representation of a complete state holding orbit, attitude
   * and mass information at a given date.
   *
   * <p>It contains an {@link Orbit orbital state} at a current
   * {@link AbsoluteDate} both handled by an {@link Orbit}, plus the current
   * mass and attitude. Orbit and state are guaranteed to be consistent in terms
   * of date and reference frame. The spacecraft state may also contain additional
   * states, which are simply named double arrays which can hold any user-defined
   * data.
   * </p>
   * <p>
   * The state can be slightly shifted to close dates. This shift is based on
   * a simple Keplerian model for orbit, a linear extrapolation for attitude
   * taking the spin rate into account and no mass change. It is <em>not</em>
   * intended as a replacement for proper orbit and attitude propagation but
   * should be sufficient for either small time shifts or coarse accuracy.
   * </p>
   * <p>
   * The instance <code>SpacecraftState</code> is guaranteed to be immutable.
   * </p>
   * @see org.orekit.propagation.numerical.NumericalPropagator
   * @author Fabien Maussion
   * @author V&eacute;ronique Pommier-Maurussane
   * @author Luc Maisonobe
   */
  public class SpacecraftState
      implements TimeStamped, TimeShiftable<SpacecraftState>, TimeInterpolable<SpacecraftState>, Serializable {
  
      /** Serializable UID. */
      private static final long serialVersionUID = 20211119L;
  
      /** Default mass. */
      private static final double DEFAULT_MASS = 1000.0;
  
      /**
       * tolerance on date comparison in {@link #checkConsistency(Orbit, Attitude)}. 100 ns
       * corresponds to sub-mm accuracy at LEO orbital velocities.
       */
      private static final double DATE_INCONSISTENCY_THRESHOLD = 100e-9;
  
      /** Orbital state. */
      private final Orbit orbit;
  
      /** Trajectory state, when it is not an orbit. */
      private final AbsolutePVCoordinates absPva;
  
      /** Attitude. */
      private final Attitude attitude;
  
     /** Current mass (kg). */
     private final double mass;
 
     /** Additional states. */
     private final DoubleArrayDictionary additional;
 
     /** Additional states derivatives.
      * @since 11.1
      */
     private final DoubleArrayDictionary additionalDot;
 
     /** Build a spacecraft state from orbit only.
      * <p>Attitude and mass are set to unspecified non-null arbitrary values.</p>
      * @param orbit the orbit
      */
     public SpacecraftState(final Orbit orbit) {
         this(orbit,
              new LofOffset(orbit.getFrame(),
                            LOFType.LVLH_CCSDS).getAttitude(orbit, orbit.getDate(), orbit.getFrame()),
              DEFAULT_MASS, (DoubleArrayDictionary) null);
     }
 
     /** Build a spacecraft state from orbit and attitude.
      * <p>Mass is set to an unspecified non-null arbitrary value.</p>
      * @param orbit the orbit
      * @param attitude attitude
      * @exception IllegalArgumentException if orbit and attitude dates
      * or frames are not equal
      */
     public SpacecraftState(final Orbit orbit, final Attitude attitude)
         throws IllegalArgumentException {
         this(orbit, attitude, DEFAULT_MASS, (DoubleArrayDictionary) null);
     }
 
     /** Create a new instance from orbit and mass.
      * <p>Attitude law is set to an unspecified default attitude.</p>
      * @param orbit the orbit
      * @param mass the mass (kg)
      */
     public SpacecraftState(final Orbit orbit, final double mass) {
         this(orbit,
              new LofOffset(orbit.getFrame(),
                            LOFType.LVLH_CCSDS).getAttitude(orbit, orbit.getDate(), orbit.getFrame()),
              mass, (DoubleArrayDictionary) null);
     }
 
     /** Build a spacecraft state from orbit, attitude and mass.
      * @param orbit the orbit
      * @param attitude attitude
      * @param mass the mass (kg)
      * @exception IllegalArgumentException if orbit and attitude dates
      * or frames are not equal
      */
     public SpacecraftState(final Orbit orbit, final Attitude attitude, final double mass)
         throws IllegalArgumentException {
         this(orbit, attitude, mass, (DoubleArrayDictionary) null);
     }
 
     /** Build a spacecraft state from orbit and additional states.
      * <p>Attitude and mass are set to unspecified non-null arbitrary values.</p>
      * @param orbit the orbit
      * @param additional additional states
      * @deprecated as of 11.1, replaced by {@link #SpacecraftState(Orbit, DoubleArrayDictionary)}
      */
     @Deprecated
     public SpacecraftState(final Orbit orbit, final Map<String, double[]> additional) {
         this(orbit, new DoubleArrayDictionary(additional));
     }
 
     /** Build a spacecraft state from orbit and additional states.
      * <p>Attitude and mass are set to unspecified non-null arbitrary values.</p>
      * @param orbit the orbit
      * @param additional additional states
      * @since 11.1
      */
     public SpacecraftState(final Orbit orbit, final DoubleArrayDictionary additional) {
         this(orbit,
              new LofOffset(orbit.getFrame(),
                            LOFType.LVLH_CCSDS).getAttitude(orbit, orbit.getDate(), orbit.getFrame()),
              DEFAULT_MASS, additional);
     }
 
     /** Build a spacecraft state from orbit, attitude and additional states.
      * <p>Mass is set to an unspecified non-null arbitrary value.</p>
      * @param orbit the orbit
      * @param attitude attitude
      * @param additional additional states
      * @exception IllegalArgumentException if orbit and attitude dates
      * or frames are not equal
      * @deprecated as of 11.1, replaced by {@link #SpacecraftState(Orbit, Attitude, DoubleArrayDictionary)}
      */
     @Deprecated
     public SpacecraftState(final Orbit orbit, final Attitude attitude, final Map<String, double[]> additional)
         throws IllegalArgumentException {
         this(orbit, attitude, new DoubleArrayDictionary(additional));
     }
 
     /** Build a spacecraft state from orbit, attitude and additional states.
      * <p>Mass is set to an unspecified non-null arbitrary value.</p>
      * @param orbit the orbit
      * @param attitude attitude
      * @param additional additional states
      * @exception IllegalArgumentException if orbit and attitude dates
      * or frames are not equal
      * @since 11.1
      */
     public SpacecraftState(final Orbit orbit, final Attitude attitude, final DoubleArrayDictionary additional)
         throws IllegalArgumentException {
         this(orbit, attitude, DEFAULT_MASS, additional);
     }
 
     /** Create a new instance from orbit, mass and additional states.
      * <p>Attitude law is set to an unspecified default attitude.</p>
      * @param orbit the orbit
      * @param mass the mass (kg)
      * @param additional additional states
      * @deprecated as of 11.1, replaced by {@link #SpacecraftState(Orbit, double, DoubleArrayDictionary)}
      */
     @Deprecated
     public SpacecraftState(final Orbit orbit, final double mass, final Map<String, double[]> additional) {
         this(orbit, mass, new DoubleArrayDictionary(additional));
     }
 
     /** Create a new instance from orbit, mass and additional states.
      * <p>Attitude law is set to an unspecified default attitude.</p>
      * @param orbit the orbit
      * @param mass the mass (kg)
      * @param additional additional states
      * @since 11.1
      */
     public SpacecraftState(final Orbit orbit, final double mass, final DoubleArrayDictionary additional) {
         this(orbit,
              new LofOffset(orbit.getFrame(), LOFType.LVLH_CCSDS).getAttitude(orbit, orbit.getDate(), orbit.getFrame()),
              mass, additional);
     }
 
     /** Build a spacecraft state from orbit, attitude, mass and additional states.
      * @param orbit the orbit
      * @param attitude attitude
      * @param mass the mass (kg)
      * @param additional additional states (may be null if no additional states are available)
      * @exception IllegalArgumentException if orbit and attitude dates
      * or frames are not equal
      * @deprecated as of 11.1, replaced by {@link #SpacecraftState(Orbit, Attitude, double, DoubleArrayDictionary)}
      */
     @Deprecated
     public SpacecraftState(final Orbit orbit, final Attitude attitude,
                            final double mass, final Map<String, double[]> additional)
         throws IllegalArgumentException {
         this(orbit, attitude, mass, new DoubleArrayDictionary(additional));
     }
 
     /** Build a spacecraft state from orbit, attitude, mass and additional states.
      * @param orbit the orbit
      * @param attitude attitude
      * @param mass the mass (kg)
      * @param additional additional states (may be null if no additional states are available)
      * @exception IllegalArgumentException if orbit and attitude dates
      * or frames are not equal
      * @since 11.1
      */
     public SpacecraftState(final Orbit orbit, final Attitude attitude,
                            final double mass, final DoubleArrayDictionary additional)
         throws IllegalArgumentException {
         this(orbit, attitude, mass, additional, null);
     }
 
     /** Build a spacecraft state from orbit, attitude, mass, additional states and derivatives.
      * @param orbit the orbit
      * @param attitude attitude
      * @param mass the mass (kg)
      * @param additional additional states (may be null if no additional states are available)
      * @param additionalDot additional states derivatives (may be null if no additional states derivatives are available)
      * @exception IllegalArgumentException if orbit and attitude dates
      * or frames are not equal
      * @since 11.1
      */
     public SpacecraftState(final Orbit orbit, final Attitude attitude, final double mass,
                            final DoubleArrayDictionary additional, final DoubleArrayDictionary additionalDot)
         throws IllegalArgumentException {
         checkConsistency(orbit, attitude);
         this.orbit      = orbit;
         this.absPva     = null;
         this.attitude   = attitude;
         this.mass       = mass;
         if (additional == null) {
             this.additional = new DoubleArrayDictionary();
         } else {
             this.additional = additional;
         }
         if (additionalDot == null) {
             this.additionalDot = new DoubleArrayDictionary();
         } else {
             this.additionalDot = new DoubleArrayDictionary(additionalDot);
         }
     }
 
 
 
     /** Build a spacecraft state from position-velocity-acceleration only.
      * <p>Attitude and mass are set to unspecified non-null arbitrary values.</p>
      * @param absPva position-velocity-acceleration
      */
     public SpacecraftState(final AbsolutePVCoordinates absPva) {
         this(absPva,
              new LofOffset(absPva.getFrame(), LOFType.LVLH_CCSDS).getAttitude(absPva, absPva.getDate(), absPva.getFrame()),
              DEFAULT_MASS, (DoubleArrayDictionary) null);
     }
 
     /** Build a spacecraft state from position-velocity-acceleration and attitude.
      * <p>Mass is set to an unspecified non-null arbitrary value.</p>
      * @param absPva position-velocity-acceleration
      * @param attitude attitude
      * @exception IllegalArgumentException if orbit and attitude dates
      * or frames are not equal
      */
     public SpacecraftState(final AbsolutePVCoordinates absPva, final Attitude attitude)
         throws IllegalArgumentException {
         this(absPva, attitude, DEFAULT_MASS, (DoubleArrayDictionary) null);
     }
 
     /** Create a new instance from position-velocity-acceleration and mass.
      * <p>Attitude law is set to an unspecified default attitude.</p>
      * @param absPva position-velocity-acceleration
      * @param mass the mass (kg)
      */
     public SpacecraftState(final AbsolutePVCoordinates absPva, final double mass) {
         this(absPva,
              new LofOffset(absPva.getFrame(), LOFType.LVLH_CCSDS).getAttitude(absPva, absPva.getDate(), absPva.getFrame()),
              mass, (DoubleArrayDictionary) null);
     }
 
     /** Build a spacecraft state from position-velocity-acceleration, attitude and mass.
      * @param absPva position-velocity-acceleration
      * @param attitude attitude
      * @param mass the mass (kg)
      * @exception IllegalArgumentException if orbit and attitude dates
      * or frames are not equal
      */
     public SpacecraftState(final AbsolutePVCoordinates absPva, final Attitude attitude, final double mass)
         throws IllegalArgumentException {
         this(absPva, attitude, mass, (DoubleArrayDictionary) null);
     }
 
     /** Build a spacecraft state from position-velocity-acceleration and additional states.
      * <p>Attitude and mass are set to unspecified non-null arbitrary values.</p>
      * @param absPva position-velocity-acceleration
      * @param additional additional states
      * @deprecated as of 11.1, replaced by {@link #SpacecraftState(AbsolutePVCoordinates, DoubleArrayDictionary)}
      */
     @Deprecated
     public SpacecraftState(final AbsolutePVCoordinates absPva, final Map<String, double[]> additional) {
         this(absPva, new DoubleArrayDictionary(additional));
     }
 
     /** Build a spacecraft state from position-velocity-acceleration and additional states.
      * <p>Attitude and mass are set to unspecified non-null arbitrary values.</p>
      * @param absPva position-velocity-acceleration
      * @param additional additional states
      * @since 11.1
      */
     public SpacecraftState(final AbsolutePVCoordinates absPva, final DoubleArrayDictionary additional) {
         this(absPva,
              new LofOffset(absPva.getFrame(), LOFType.LVLH_CCSDS).getAttitude(absPva, absPva.getDate(), absPva.getFrame()),
              DEFAULT_MASS, additional);
     }
 
     /** Build a spacecraft state from position-velocity-acceleration, attitude and additional states.
      * <p>Mass is set to an unspecified non-null arbitrary value.</p>
      * @param absPva position-velocity-acceleration
      * @param attitude attitude
      * @param additional additional states
      * @exception IllegalArgumentException if orbit and attitude dates
      * or frames are not equal
      * @deprecated as of 11.1, replaced by {@link #SpacecraftState(AbsolutePVCoordinates, Attitude, DoubleArrayDictionary)}
      */
     @Deprecated
     public SpacecraftState(final AbsolutePVCoordinates absPva, final Attitude attitude, final Map<String, double[]> additional)
         throws IllegalArgumentException {
         this(absPva, attitude, new DoubleArrayDictionary(additional));
     }
 
     /** Build a spacecraft state from position-velocity-acceleration, attitude and additional states.
      * <p>Mass is set to an unspecified non-null arbitrary value.</p>
      * @param absPva position-velocity-acceleration
      * @param attitude attitude
      * @param additional additional states
      * @exception IllegalArgumentException if orbit and attitude dates
      * or frames are not equal
      * @since 11.1
      */
     public SpacecraftState(final AbsolutePVCoordinates absPva, final Attitude attitude, final DoubleArrayDictionary additional)
         throws IllegalArgumentException {
         this(absPva, attitude, DEFAULT_MASS, additional);
     }
 
     /** Create a new instance from position-velocity-acceleration, mass and additional states.
      * <p>Attitude law is set to an unspecified default attitude.</p>
      * @param absPva position-velocity-acceleration
      * @param mass the mass (kg)
      * @param additional additional states
      * @deprecated as of 11.1, replaced by {@link #SpacecraftState(AbsolutePVCoordinates, double, DoubleArrayDictionary)}
      */
     @Deprecated
     public SpacecraftState(final AbsolutePVCoordinates absPva, final double mass, final Map<String, double[]> additional) {
         this(absPva, mass, new DoubleArrayDictionary(additional));
     }
 
     /** Create a new instance from position-velocity-acceleration, mass and additional states.
      * <p>Attitude law is set to an unspecified default attitude.</p>
      * @param absPva position-velocity-acceleration
      * @param mass the mass (kg)
      * @param additional additional states
      * @since 11.1
      */
     public SpacecraftState(final AbsolutePVCoordinates absPva, final double mass, final DoubleArrayDictionary additional) {
         this(absPva,
              new LofOffset(absPva.getFrame(), LOFType.LVLH_CCSDS).getAttitude(absPva, absPva.getDate(), absPva.getFrame()),
              mass, additional);
     }
 
     /** Build a spacecraft state from position-velocity-acceleration, attitude, mass and additional states.
      * @param absPva position-velocity-acceleration
      * @param attitude attitude
      * @param mass the mass (kg)
      * @param additional additional states (may be null if no additional states are available)
      * @exception IllegalArgumentException if orbit and attitude dates
      * or frames are not equal
      * @deprecated as of 11.1, replaced by {@link #SpacecraftState(AbsolutePVCoordinates, Attitude, double, DoubleArrayDictionary)}
      */
     public SpacecraftState(final AbsolutePVCoordinates absPva, final Attitude attitude,
                            final double mass, final Map<String, double[]> additional)
         throws IllegalArgumentException {
         this(absPva, attitude, mass, new DoubleArrayDictionary(additional));
     }
 
     /** Build a spacecraft state from position-velocity-acceleration, attitude, mass and additional states.
      * @param absPva position-velocity-acceleration
      * @param attitude attitude
      * @param mass the mass (kg)
      * @param additional additional states (may be null if no additional states are available)
      * @exception IllegalArgumentException if orbit and attitude dates
      * or frames are not equal
      * @since 11.1
      */
     public SpacecraftState(final AbsolutePVCoordinates absPva, final Attitude attitude,
                            final double mass, final DoubleArrayDictionary additional)
         throws IllegalArgumentException {
         this(absPva, attitude, mass, additional, null);
     }
 
     /** Build a spacecraft state from position-velocity-acceleration, attitude, mass and additional states and derivatives.
      * @param absPva position-velocity-acceleration
      * @param attitude attitude
      * @param mass the mass (kg)
      * @param additional additional states (may be null if no additional states are available)
      * @param additionalDot additional states derivatives(may be null if no additional states derivativesare available)
      * @exception IllegalArgumentException if orbit and attitude dates
      * or frames are not equal
      * @since 11.1
      */
     public SpacecraftState(final AbsolutePVCoordinates absPva, final Attitude attitude, final double mass,
                            final DoubleArrayDictionary additional, final DoubleArrayDictionary additionalDot)
         throws IllegalArgumentException {
         checkConsistency(absPva, attitude);
         this.orbit      = null;
         this.absPva     = absPva;
         this.attitude   = attitude;
         this.mass       = mass;
         if (additional == null) {
             this.additional = new DoubleArrayDictionary();
         } else {
             this.additional = new DoubleArrayDictionary(additional);
         }
         if (additionalDot == null) {
             this.additionalDot = new DoubleArrayDictionary();
         } else {
             this.additionalDot = new DoubleArrayDictionary(additionalDot);
         }
     }
 
     /** Add an additional state.
      * <p>
      * {@link SpacecraftState SpacecraftState} instances are immutable,
      * so this method does <em>not</em> change the instance, but rather
      * creates a new instance, which has the same orbit, attitude, mass
      * and additional states as the original instance, except it also
      * has the specified state. If the original instance already had an
      * additional state with the same name, it will be overridden. If it
      * did not have any additional state with that name, the new instance
      * will have one more additional state than the original instance.
      * </p>
      * @param name name of the additional state (names containing "orekit"
      * with any case are reserved for the library internal use)
      * @param value value of the additional state
      * @return a new instance, with the additional state added
      * @see #hasAdditionalState(String)
      * @see #getAdditionalState(String)
      * @see #getAdditionalStates()
      */
     public SpacecraftState addAdditionalState(final String name, final double... value) {
         final DoubleArrayDictionary newDict = new DoubleArrayDictionary(additional);
         newDict.put(name, value.clone());
         if (absPva == null) {
             return new SpacecraftState(orbit, attitude, mass, newDict, additionalDot);
         } else {
             return new SpacecraftState(absPva, attitude, mass, newDict, additionalDot);
         }
     }
 
     /** Add an additional state derivative.
      * <p>
      * {@link SpacecraftState SpacecraftState} instances are immutable,
      * so this method does <em>not</em> change the instance, but rather
      * creates a new instance, which has the same components as the original
      * instance, except it also has the specified state derivative. If the
      * original instance already had an additional state derivative with the
      * same name, it will be overridden. If it did not have any additional
      * state derivative with that name, the new instance will have one more
      * additional state derivative than the original instance.
      * </p>
      * @param name name of the additional state derivative (names containing "orekit"
      * with any case are reserved for the library internal use)
      * @param value value of the additional state derivative
      * @return a new instance, with the additional state added
      * @see #hasAdditionalStateDerivative(String)
      * @see #getAdditionalStateDerivative(String)
      * @see #getAdditionalStatesDerivatives()
      * @since 11.1
      */
     public SpacecraftState addAdditionalStateDerivative(final String name, final double... value) {
         final DoubleArrayDictionary newDict = new DoubleArrayDictionary(additionalDot);
         newDict.put(name, value.clone());
         if (absPva == null) {
             return new SpacecraftState(orbit, attitude, mass, additional, newDict);
         } else {
             return new SpacecraftState(absPva, attitude, mass, additional, newDict);
         }
     }
 
     /** Check orbit and attitude dates are equal.
      * @param orbit the orbit
      * @param attitude attitude
      * @exception IllegalArgumentException if orbit and attitude dates
      * are not equal
      */
     private static void checkConsistency(final Orbit orbit, final Attitude attitude)
         throws IllegalArgumentException {
         if (FastMath.abs(orbit.getDate().durationFrom(attitude.getDate())) >
             DATE_INCONSISTENCY_THRESHOLD) {
             throw new OrekitIllegalArgumentException(OrekitMessages.ORBIT_AND_ATTITUDE_DATES_MISMATCH,
                                                      orbit.getDate(), attitude.getDate());
         }
         if (orbit.getFrame() != attitude.getReferenceFrame()) {
             throw new OrekitIllegalArgumentException(OrekitMessages.FRAMES_MISMATCH,
                                                      orbit.getFrame().getName(),
                                                      attitude.getReferenceFrame().getName());
         }
     }
 
     /** Check if the state contains an orbit part.
      * <p>
      * A state contains either an {@link AbsolutePVCoordinates absolute
      * position-velocity-acceleration} or an {@link Orbit orbit}.
      * </p>
      * @return true if state contains an orbit (in which case {@link #getOrbit()}
      * will not throw an exception), or false if the state contains an
      * absolut position-velocity-acceleration (in which case {@link #getAbsPVA()}
      * will not throw an exception)
      */
     public boolean isOrbitDefined() {
         return orbit != null;
     }
 
     /** Check AbsolutePVCoordinates and attitude dates are equal.
      * @param absPva position-velocity-acceleration
      * @param attitude attitude
      * @exception IllegalArgumentException if orbit and attitude dates
      * are not equal
      */
     private static void checkConsistency(final AbsolutePVCoordinates absPva, final Attitude attitude)
         throws IllegalArgumentException {
         if (FastMath.abs(absPva.getDate().durationFrom(attitude.getDate())) >
             DATE_INCONSISTENCY_THRESHOLD) {
             throw new OrekitIllegalArgumentException(OrekitMessages.ORBIT_AND_ATTITUDE_DATES_MISMATCH,
                                                      absPva.getDate(), attitude.getDate());
         }
         if (absPva.getFrame() != attitude.getReferenceFrame()) {
             throw new OrekitIllegalArgumentException(OrekitMessages.FRAMES_MISMATCH,
                                                      absPva.getFrame().getName(),
                                                      attitude.getReferenceFrame().getName());
         }
     }
 
     /** Get a time-shifted state.
      * <p>
      * The state can be slightly shifted to close dates. This shift is based on
      * simple models. For orbits, the model is a Keplerian one if no derivatives
      * are available in the orbit, or Keplerian plus quadratic effect of the
      * non-Keplerian acceleration if derivatives are available. For attitude,
      * a polynomial model is used. Neither mass nor additional states change.
      * Shifting is <em>not</em> intended as a replacement for proper orbit
      * and attitude propagation but should be sufficient for small time shifts
      * or coarse accuracy.
      * </p>
      * <p>
      * As a rough order of magnitude, the following table shows the extrapolation
      * errors obtained between this simple shift method and an {@link
      * org.orekit.propagation.numerical.NumericalPropagator numerical
      * propagator} for a low Earth Sun Synchronous Orbit, with a 20x20 gravity field,
      * Sun and Moon third bodies attractions, drag and solar radiation pressure.
      * Beware that these results will be different for other orbits.
      * </p>
      * <table border="1">
      * <caption>Extrapolation Error</caption>
      * <tr style="background-color: #ccccff"><th>interpolation time (s)</th>
      * <th>position error without derivatives (m)</th><th>position error with derivatives (m)</th></tr>
      * <tr><td style="background-color: #eeeeff; padding:5px"> 60</td><td>  18</td><td> 1.1</td></tr>
      * <tr><td style="background-color: #eeeeff; padding:5px">120</td><td>  72</td><td> 9.1</td></tr>
      * <tr><td style="background-color: #eeeeff; padding:5px">300</td><td> 447</td><td> 140</td></tr>
      * <tr><td style="background-color: #eeeeff; padding:5px">600</td><td>1601</td><td>1067</td></tr>
      * <tr><td style="background-color: #eeeeff; padding:5px">900</td><td>3141</td><td>3307</td></tr>
      * </table>
      * @param dt time shift in seconds
      * @return a new state, shifted with respect to the instance (which is immutable)
      * except for the mass and additional states which stay unchanged
      */
     public SpacecraftState shiftedBy(final double dt) {
         if (absPva == null) {
             return new SpacecraftState(orbit.shiftedBy(dt), attitude.shiftedBy(dt),
                                        mass, shiftAdditional(dt), additionalDot);
         } else {
             return new SpacecraftState(absPva.shiftedBy(dt), attitude.shiftedBy(dt),
                                        mass, shiftAdditional(dt), additionalDot);
         }
     }
 
     /** Shift additional states.
      * @param dt time shift in seconds
      * @return shifted additional states
      * @since 11.1.1
      */
     private DoubleArrayDictionary shiftAdditional(final double dt) {
 
         // fast handling when there are no derivatives at all
         if (additionalDot.size() == 0) {
             return additional;
         }
 
         // there are derivatives, we need to take them into account in the additional state
         final DoubleArrayDictionary shifted = new DoubleArrayDictionary(additional);
         for (final DoubleArrayDictionary.Entry dotEntry : additionalDot.getData()) {
             final DoubleArrayDictionary.Entry entry = shifted.getEntry(dotEntry.getKey());
             if (entry != null) {
                 entry.scaledIncrement(dt, dotEntry);
             }
         }
 
         return shifted;
 
     }
 
     /** {@inheritDoc}
      * <p>
      * The additional states that are interpolated are the ones already present
      * in the instance. The sample instances must therefore have at least the same
      * additional states has the instance. They may have more additional states,
      * but the extra ones will be ignored.
      * </p>
      * <p>
      * The instance and all the sample instances <em>must</em> be based on similar
      * trajectory data, i.e. they must either all be based on orbits or all be based
      * on absolute position-velocity-acceleration. Any inconsistency will trigger
      * an {@link OrekitIllegalStateException}.
      * </p>
      * <p>
      * As this implementation of interpolation is polynomial, it should be used only
      * with small samples (about 10-20 points) in order to avoid <a
      * href="http://en.wikipedia.org/wiki/Runge%27s_phenomenon">Runge's phenomenon</a>
      * and numerical problems (including NaN appearing).
      * </p>
      * @exception OrekitIllegalStateException if some instances are not based on
      * similar trajectory data
      */
     public SpacecraftState interpolate(final AbsoluteDate date,
                                        final Stream<SpacecraftState> sample) {
 
         // prepare interpolators
         final List<Orbit> orbits;
         final List<AbsolutePVCoordinates> absPvas;
         if (isOrbitDefined()) {
             orbits  = new ArrayList<Orbit>();
             absPvas = null;
         } else {
             orbits  = null;
             absPvas = new ArrayList<AbsolutePVCoordinates>();
         }
         final List<Attitude> attitudes = new ArrayList<>();
         final HermiteInterpolator massInterpolator = new HermiteInterpolator();
         final List<DoubleArrayDictionary.Entry> addionalEntries = additional.getData();
         final Map<String, HermiteInterpolator> additionalInterpolators =
                 new HashMap<String, HermiteInterpolator>(addionalEntries.size());
         for (final DoubleArrayDictionary.Entry entry : addionalEntries) {
             additionalInterpolators.put(entry.getKey(), new HermiteInterpolator());
         }
         final List<DoubleArrayDictionary.Entry> additionalDotEntries = additionalDot.getData();
         final Map<String, HermiteInterpolator> additionalDotInterpolators =
                 new HashMap<String, HermiteInterpolator>(additionalDotEntries.size());
         for (final DoubleArrayDictionary.Entry entry : additionalDotEntries) {
             additionalDotInterpolators.put(entry.getKey(), new HermiteInterpolator());
         }
 
         // extract sample data
         sample.forEach(state -> {
             final double deltaT = state.getDate().durationFrom(date);
             if (isOrbitDefined()) {
                 orbits.add(state.getOrbit());
             } else {
                 absPvas.add(state.getAbsPVA());
             }
             attitudes.add(state.getAttitude());
             massInterpolator.addSamplePoint(deltaT,
                                             new double[] {
                                                 state.getMass()
                                                 });
             for (final Map.Entry<String, HermiteInterpolator> entry : additionalInterpolators.entrySet()) {
                 entry.getValue().addSamplePoint(deltaT, state.getAdditionalState(entry.getKey()));
             }
             for (final Map.Entry<String, HermiteInterpolator> entry : additionalDotInterpolators.entrySet()) {
                 entry.getValue().addSamplePoint(deltaT, state.getAdditionalStateDerivative(entry.getKey()));
             }
 
         });
 
         // perform interpolations
         final Orbit interpolatedOrbit;
         final AbsolutePVCoordinates interpolatedAbsPva;
         if (isOrbitDefined()) {
             interpolatedOrbit  = orbit.interpolate(date, orbits);
             interpolatedAbsPva = null;
         } else {
             interpolatedOrbit  = null;
             interpolatedAbsPva = absPva.interpolate(date, absPvas);
         }
         final Attitude interpolatedAttitude = attitude.interpolate(date, attitudes);
         final double interpolatedMass       = massInterpolator.value(0)[0];
         final DoubleArrayDictionary interpolatedAdditional;
         if (additionalInterpolators.isEmpty()) {
             interpolatedAdditional = null;
         } else {
             interpolatedAdditional = new DoubleArrayDictionary(additionalInterpolators.size());
             for (final Map.Entry<String, HermiteInterpolator> entry : additionalInterpolators.entrySet()) {
                 interpolatedAdditional.put(entry.getKey(), entry.getValue().value(0));
             }
         }
         final DoubleArrayDictionary interpolatedAdditionalDot;
         if (additionalDotInterpolators.isEmpty()) {
             interpolatedAdditionalDot = null;
         } else {
             interpolatedAdditionalDot = new DoubleArrayDictionary(additionalDotInterpolators.size());
             for (final Map.Entry<String, HermiteInterpolator> entry : additionalDotInterpolators.entrySet()) {
                 interpolatedAdditionalDot.put(entry.getKey(), entry.getValue().value(0));
             }
         }
 
         // create the complete interpolated state
         if (isOrbitDefined()) {
             return new SpacecraftState(interpolatedOrbit, interpolatedAttitude, interpolatedMass,
                                        interpolatedAdditional, interpolatedAdditionalDot);
         } else {
             return new SpacecraftState(interpolatedAbsPva, interpolatedAttitude, interpolatedMass,
                                        interpolatedAdditional, interpolatedAdditionalDot);
         }
 
     }
 
     /** Get the absolute position-velocity-acceleration.
      * <p>
      * A state contains either an {@link AbsolutePVCoordinates absolute
      * position-velocity-acceleration} or an {@link Orbit orbit}. Which
      * one is present can be checked using {@link #isOrbitDefined()}.
      * </p>
      * @return absolute position-velocity-acceleration
      * @exception OrekitIllegalStateException if position-velocity-acceleration is null,
      * which mean the state rather contains an {@link Orbit}
      * @see #isOrbitDefined()
      * @see #getOrbit()
      */
     public AbsolutePVCoordinates getAbsPVA() throws OrekitIllegalStateException {
         if (absPva == null) {
             throw new OrekitIllegalStateException(OrekitMessages.UNDEFINED_ABSOLUTE_PVCOORDINATES);
         }
         return absPva;
     }
 
     /** Get the current orbit.
      * <p>
      * A state contains either an {@link AbsolutePVCoordinates absolute
      * position-velocity-acceleration} or an {@link Orbit orbit}. Which
      * one is present can be checked using {@link #isOrbitDefined()}.
      * </p>
      * @return the orbit
      * @exception OrekitIllegalStateException if orbit is null,
      * which means the state rather contains an {@link AbsolutePVCoordinates absolute
      * position-velocity-acceleration}
      * @see #isOrbitDefined()
      * @see #getAbsPVA()
      */
     public Orbit getOrbit() throws OrekitIllegalStateException {
         if (orbit == null) {
             throw new OrekitIllegalStateException(OrekitMessages.UNDEFINED_ORBIT);
         }
         return orbit;
     }
 
     /** Get the date.
      * @return date
      */
     public AbsoluteDate getDate() {
         return (absPva == null) ? orbit.getDate() : absPva.getDate();
     }
 
     /** Get the defining frame.
      * @return the frame in which state is defined
      */
     public Frame getFrame() {
         return (absPva == null) ? orbit.getFrame() : absPva.getFrame();
     }
 
     /** Check if an additional state is available.
      * @param name name of the additional state
      * @return true if the additional state is available
      * @see #addAdditionalState(String, double[])
      * @see #getAdditionalState(String)
      * @see #getAdditionalStates()
      */
     public boolean hasAdditionalState(final String name) {
         return additional.getEntry(name) != null;
     }
 
     /** Check if an additional state derivative is available.
      * @param name name of the additional state derivative
      * @return true if the additional state derivative is available
      * @see #addAdditionalStateDerivative(String, double[])
      * @see #getAdditionalStateDerivative(String)
      * @see #getAdditionalStatesDerivatives()
      * @since 11.1
      */
     public boolean hasAdditionalStateDerivative(final String name) {
         return additionalDot.getEntry(name) != null;
     }
 
     /** Check if two instances have the same set of additional states available.
      * <p>
      * Only the names and dimensions of the additional states are compared,
      * not their values.
      * </p>
      * @param state state to compare to instance
      * @exception MathIllegalStateException if an additional state does not have
      * the same dimension in both states
      */
     public void ensureCompatibleAdditionalStates(final SpacecraftState state)
         throws MathIllegalStateException {
 
         // check instance additional states is a subset of the other one
         for (final DoubleArrayDictionary.Entry entry : additional.getData()) {
             final double[] other = state.additional.get(entry.getKey());
             if (other == null) {
                 throw new OrekitException(OrekitMessages.UNKNOWN_ADDITIONAL_STATE,
                                           entry.getKey());
             }
             if (other.length != entry.getValue().length) {
                 throw new MathIllegalStateException(LocalizedCoreFormats.DIMENSIONS_MISMATCH,
                                                     other.length, entry.getValue().length);
             }
         }
 
         // check instance additional states derivatives is a subset of the other one
         for (final DoubleArrayDictionary.Entry entry : additionalDot.getData()) {
             final double[] other = state.additionalDot.get(entry.getKey());
             if (other == null) {
                 throw new OrekitException(OrekitMessages.UNKNOWN_ADDITIONAL_STATE,
                                           entry.getKey());
             }
             if (other.length != entry.getValue().length) {
                 throw new MathIllegalStateException(LocalizedCoreFormats.DIMENSIONS_MISMATCH,
                                                     other.length, entry.getValue().length);
             }
         }
 
         if (state.additional.size() > additional.size()) {
             // the other state has more additional states
             for (final DoubleArrayDictionary.Entry entry : state.additional.getData()) {
                 if (additional.getEntry(entry.getKey()) == null) {
                     throw new OrekitException(OrekitMessages.UNKNOWN_ADDITIONAL_STATE,
                                               entry.getKey());
                 }
             }
         }
 
         if (state.additionalDot.size() > additionalDot.size()) {
             // the other state has more additional states
             for (final DoubleArrayDictionary.Entry entry : state.additionalDot.getData()) {
                 if (additionalDot.getEntry(entry.getKey()) == null) {
                     throw new OrekitException(OrekitMessages.UNKNOWN_ADDITIONAL_STATE,
                                               entry.getKey());
                 }
             }
         }
 
     }
 
     /** Get an additional state.
      * @param name name of the additional state
      * @return value of the additional state
      * @see #addAdditionalState(String, double[])
      * @see #hasAdditionalState(String)
      * @see #getAdditionalStates()
      */
     public double[] getAdditionalState(final String name) {
         final DoubleArrayDictionary.Entry entry = additional.getEntry(name);
         if (entry == null) {
             throw new OrekitException(OrekitMessages.UNKNOWN_ADDITIONAL_STATE, name);
         }
         return entry.getValue();
     }
 
     /** Get an additional state derivative.
      * @param name name of the additional state derivative
      * @return value of the additional state derivative
      * @see #addAdditionalStateDerivative(String, double[])
      * @see #hasAdditionalStateDerivative(String)
      * @see #getAdditionalStatesDerivatives()
      * @since 11.1
      */
     public double[] getAdditionalStateDerivative(final String name) {
         final DoubleArrayDictionary.Entry entry = additionalDot.getEntry(name);
         if (entry == null) {
             throw new OrekitException(OrekitMessages.UNKNOWN_ADDITIONAL_STATE, name);
         }
         return entry.getValue();
     }
 
     /** Get an unmodifiable map of additional states.
      * @return unmodifiable map of additional states
      * @see #addAdditionalState(String, double[])
      * @see #hasAdditionalState(String)
      * @see #getAdditionalState(String)
      * @deprecated as of 11.1, replaced by {@link #getAdditionalStatesValues()}
      */
     @Deprecated
     public Map<String, double[]> getAdditionalStates() {
         return getAdditionalStatesValues().toMap();
     }
 
     /** Get an unmodifiable map of additional states.
      * @return unmodifiable map of additional states
      * @see #addAdditionalState(String, double[])
      * @see #hasAdditionalState(String)
      * @see #getAdditionalState(String)
      * @since 11.1
      */
     public DoubleArrayDictionary getAdditionalStatesValues() {
         return additional.unmodifiableView();
     }
 
     /** Get an unmodifiable map of additional states derivatives.
      * @return unmodifiable map of additional states derivatives
      * @see #addAdditionalStateDerivative(String, double[])
      * @see #hasAdditionalStateDerivative(String)
      * @see #getAdditionalStateDerivative(String)
      * @since 11.1
      */
     public DoubleArrayDictionary getAdditionalStatesDerivatives() {
         return additionalDot.unmodifiableView();
     }
 
     /** Compute the transform from state defining frame to spacecraft frame.
      * <p>The spacecraft frame origin is at the point defined by the orbit
      * (or absolute position-velocity-acceleration), and its orientation is
      * defined by the attitude.</p>
      * @return transform from specified frame to current spacecraft frame
      */
     public Transform toTransform() {
         final TimeStampedPVCoordinates pv = getPVCoordinates();
         return new Transform(pv.getDate(),
                              new Transform(pv.getDate(), pv.negate()),
                              new Transform(pv.getDate(), attitude.getOrientation()));
     }
 
     /** Get the central attraction coefficient.
      * @return mu central attraction coefficient (m^3/s^2), or {code Double.NaN} if the
      * state is contains an absolute position-velocity-acceleration rather than an orbit
      */
     public double getMu() {
         return (absPva == null) ? orbit.getMu() : Double.NaN;
     }
 
     /** Get the Keplerian period.
      * <p>The Keplerian period is computed directly from semi major axis
      * and central acceleration constant.</p>
      * @return keplerian period in seconds, or {code Double.NaN} if the
      * state is contains an absolute position-velocity-acceleration rather
      * than an orbit
      */
     public double getKeplerianPeriod() {
         return (absPva == null) ? orbit.getKeplerianPeriod() : Double.NaN;
     }
 
     /** Get the Keplerian mean motion.
      * <p>The Keplerian mean motion is computed directly from semi major axis
      * and central acceleration constant.</p>
      * @return keplerian mean motion in radians per second, or {code Double.NaN} if the
      * state is contains an absolute position-velocity-acceleration rather
      * than an orbit
      */
     public double getKeplerianMeanMotion() {
         return (absPva == null) ? orbit.getKeplerianMeanMotion() : Double.NaN;
     }
 
     /** Get the semi-major axis.
      * @return semi-major axis (m), or {code Double.NaN} if the
      * state is contains an absolute position-velocity-acceleration rather
      * than an orbit
      */
     public double getA() {
         return (absPva == null) ? orbit.getA() : Double.NaN;
     }
 
     /** Get the first component of the eccentricity vector (as per equinoctial parameters).
      * @return e cos(ω + Ω), first component of eccentricity vector, or {code Double.NaN} if the
      * state is contains an absolute position-velocity-acceleration rather
      * than an orbit
      * @see #getE()
      */
     public double getEquinoctialEx() {
         return (absPva == null) ? orbit.getEquinoctialEx() : Double.NaN;
     }
 
     /** Get the second component of the eccentricity vector (as per equinoctial parameters).
      * @return e sin(ω + Ω), second component of the eccentricity vector, or {code Double.NaN} if the
      * state is contains an absolute position-velocity-acceleration rather
      * than an orbit
      * @see #getE()
      */
     public double getEquinoctialEy() {
         return (absPva == null) ? orbit.getEquinoctialEy() : Double.NaN;
     }
 
     /** Get the first component of the inclination vector (as per equinoctial parameters).
      * @return tan(i/2) cos(Ω), first component of the inclination vector, or {code Double.NaN} if the
      * state is contains an absolute position-velocity-acceleration rather
      * than an orbit
      * @see #getI()
      */
     public double getHx() {
         return (absPva == null) ? orbit.getHx() : Double.NaN;
     }
 
     /** Get the second component of the inclination vector (as per equinoctial parameters).
      * @return tan(i/2) sin(Ω), second component of the inclination vector, or {code Double.NaN} if the
      * state is contains an absolute position-velocity-acceleration rather
      * than an orbit
      * @see #getI()
      */
     public double getHy() {
         return (absPva == null) ? orbit.getHy() : Double.NaN;
     }
 
     /** Get the true latitude argument (as per equinoctial parameters).
      * @return v + ω + Ω true longitude argument (rad), or {code Double.NaN} if the
      * state is contains an absolute position-velocity-acceleration rather
      * than an orbit
      * @see #getLE()
      * @see #getLM()
      */
     public double getLv() {
         return (absPva == null) ? orbit.getLv() : Double.NaN;
     }
 
     /** Get the eccentric latitude argument (as per equinoctial parameters).
      * @return E + ω + Ω eccentric longitude argument (rad), or {code Double.NaN} if the
      * state is contains an absolute position-velocity-acceleration rather
      * than an orbit
      * @see #getLv()
      * @see #getLM()
      */
     public double getLE() {
         return (absPva == null) ? orbit.getLE() : Double.NaN;
     }
 
     /** Get the mean longitude argument (as per equinoctial parameters).
      * @return M + ω + Ω mean latitude argument (rad), or {code Double.NaN} if the
      * state is contains an absolute position-velocity-acceleration rather
      * than an orbit
      * @see #getLv()
      * @see #getLE()
      */
     public double getLM() {
         return (absPva == null) ? orbit.getLM() : Double.NaN;
     }
 
     // Additional orbital elements
 
     /** Get the eccentricity.
      * @return eccentricity, or {code Double.NaN} if the
      * state is contains an absolute position-velocity-acceleration rather
      * than an orbit
      * @see #getEquinoctialEx()
      * @see #getEquinoctialEy()
      */
     public double getE() {
         return (absPva == null) ? orbit.getE() : Double.NaN;
     }
 
     /** Get the inclination.
      * @return inclination (rad)
      * @see #getHx()
      * @see #getHy()
      */
     public double getI() {
         return (absPva == null) ? orbit.getI() : Double.NaN;
     }
 
     /** Get the {@link TimeStampedPVCoordinates} in orbit definition frame.
      * <p>
      * Compute the position and velocity of the satellite. This method caches its
      * results, and recompute them only when the method is called with a new value
      * for mu. The result is provided as a reference to the internally cached
      * {@link TimeStampedPVCoordinates}, so the caller is responsible to copy it in a separate
      * {@link TimeStampedPVCoordinates} if it needs to keep the value for a while.
      * </p>
      * @return pvCoordinates in orbit definition frame
      */
     public TimeStampedPVCoordinates getPVCoordinates() {
         return (absPva == null) ? orbit.getPVCoordinates() : absPva.getPVCoordinates();
     }
 
     /** Get the {@link TimeStampedPVCoordinates} in given output frame.
      * <p>
      * Compute the position and velocity of the satellite. This method caches its
      * results, and recompute them only when the method is called with a new value
      * for mu. The result is provided as a reference to the internally cached
      * {@link TimeStampedPVCoordinates}, so the caller is responsible to copy it in a separate
      * {@link TimeStampedPVCoordinates} if it needs to keep the value for a while.
      * </p>
      * @param outputFrame frame in which coordinates should be defined
      * @return pvCoordinates in orbit definition frame
      */
     public TimeStampedPVCoordinates getPVCoordinates(final Frame outputFrame) {
         return (absPva == null) ? orbit.getPVCoordinates(outputFrame) : absPva.getPVCoordinates(outputFrame);
     }
 
     /** Get the attitude.
      * @return the attitude.
      */
     public Attitude getAttitude() {
         return attitude;
     }
 
     /** Gets the current mass.
      * @return the mass (kg)
      */
     public double getMass() {
         return mass;
     }
 
     /** Replace the instance with a data transfer object for serialization.
      * @return data transfer object that will be serialized
      */
     private Object writeReplace() {
         return isOrbitDefined() ? new DTOO(this) : new DTOA(this);
     }
 
     /** Internal class used only for serialization. */
     private static class DTOO implements Serializable {
 
         /** Serializable UID. */
         private static final long serialVersionUID = 20211121L;
 
         /** Orbit. */
         private final Orbit orbit;
 
         /** Attitude and mass double values. */
         private double[] d;
 
         /** Additional states. */
         private final DoubleArrayDictionary additional;
 
         /** Additional states derivatives. */
         private final DoubleArrayDictionary additionalDot;
 
         /** Simple constructor.
          * @param state instance to serialize
          */
         private DTOO(final SpacecraftState state) {
 
             this.orbit         = state.orbit;
             this.additional    = state.additional.getData().isEmpty()    ? null : state.additional;
             this.additionalDot = state.additionalDot.getData().isEmpty() ? null : state.additionalDot;
 
             final Rotation rotation             = state.attitude.getRotation();
             final Vector3D spin                 = state.attitude.getSpin();
             final Vector3D rotationAcceleration = state.attitude.getRotationAcceleration();
             this.d = new double[] {
                 rotation.getQ0(), rotation.getQ1(), rotation.getQ2(), rotation.getQ3(),
                 spin.getX(), spin.getY(), spin.getZ(),
                 rotationAcceleration.getX(), rotationAcceleration.getY(), rotationAcceleration.getZ(),
                 state.mass
             };
 
         }
 
         /** Replace the de-serialized data transfer object with a {@link SpacecraftState}.
          * @return replacement {@link SpacecraftState}
          */
         private Object readResolve() {
             return new SpacecraftState(orbit,
                                        new Attitude(orbit.getFrame(),
                                                     new TimeStampedAngularCoordinates(orbit.getDate(),
                                                                                       new Rotation(d[0], d[1], d[2], d[3], false),
                                                                                       new Vector3D(d[4], d[5], d[6]),
                                                                                       new Vector3D(d[7], d[8], d[9]))),
                                        d[10], additional, additionalDot);
         }
 
     }
 
     /** Internal class used only for serialization. */
     private static class DTOA implements Serializable {
 
         /** Serializable UID. */
         private static final long serialVersionUID = 20211121L;
 
         /** Absolute position-velocity-acceleration. */
         private final AbsolutePVCoordinates absPva;
 
         /** Attitude and mass double values. */
         private double[] d;
 
         /** Additional states. */
         private final DoubleArrayDictionary additional;
 
         /** Additional states derivatives. */
         private final DoubleArrayDictionary additionalDot;
 
         /** Simple constructor.
          * @param state instance to serialize
          */
         private DTOA(final SpacecraftState state) {
 
             this.absPva        = state.absPva;
             this.additional    = state.additional.getData().isEmpty()    ? null : state.additional;
             this.additionalDot = state.additionalDot.getData().isEmpty() ? null : state.additionalDot;
 
             final Rotation rotation             = state.attitude.getRotation();
             final Vector3D spin                 = state.attitude.getSpin();
             final Vector3D rotationAcceleration = state.attitude.getRotationAcceleration();
             this.d = new double[] {
                 rotation.getQ0(), rotation.getQ1(), rotation.getQ2(), rotation.getQ3(),
                 spin.getX(), spin.getY(), spin.getZ(),
                 rotationAcceleration.getX(), rotationAcceleration.getY(), rotationAcceleration.getZ(),
                 state.mass
             };
 
         }
 
         /** Replace the deserialized data transfer object with a {@link SpacecraftState}.
          * @return replacement {@link SpacecraftState}
          */
         private Object readResolve() {
             return new SpacecraftState(absPva,
                                        new Attitude(absPva.getFrame(),
                                                     new TimeStampedAngularCoordinates(absPva.getDate(),
                                                                                       new Rotation(d[0], d[1], d[2], d[3], false),
                                                                                       new Vector3D(d[4], d[5], d[6]),
                                                                                       new Vector3D(d[7], d[8], d[9]))),
                                        d[10], additional, additionalDot);
         }
     }
 
     @Override
     public String toString() {
         return "SpacecraftState{" +
                 "orbit=" + orbit +
                 ", attitude=" + attitude +
                 ", mass=" + mass +
                 ", additional=" + additional +
                 ", additionalDot=" + additionalDot +
                 '}';
     }
 }