/* Copyright 2002-2025 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,
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  package org.orekit.propagation.analytical.tle;
  
  
  import java.util.List;
  
  import org.hipparchus.CalculusFieldElement;
  import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
  import org.hipparchus.util.FastMath;
  import org.hipparchus.util.MathUtils;
  import org.hipparchus.util.Pair;
  import org.orekit.annotation.DefaultDataContext;
  import org.orekit.attitudes.AttitudeProvider;
  import org.orekit.attitudes.FieldAttitude;
  import org.orekit.attitudes.FrameAlignedProvider;
  import org.orekit.data.DataContext;
  import org.orekit.errors.OrekitException;
  import org.orekit.errors.OrekitMessages;
  import org.orekit.frames.Frame;
  import org.orekit.orbits.FieldCartesianOrbit;
  import org.orekit.orbits.FieldOrbit;
  import org.orekit.propagation.FieldSpacecraftState;
  import org.orekit.propagation.analytical.FieldAbstractAnalyticalPropagator;
  import org.orekit.propagation.analytical.tle.generation.TleGenerationAlgorithm;
  import org.orekit.time.FieldAbsoluteDate;
  import org.orekit.time.TimeScale;
  import org.orekit.utils.FieldPVCoordinates;
  import org.orekit.utils.PVCoordinates;
  import org.orekit.utils.ParameterDriver;
  import org.orekit.utils.TimeSpanMap;
  
  
  /** This class provides elements to propagate TLE's.
   * <p>
   * The models used are SGP4 and SDP4, initially proposed by NORAD as the unique convenient
   * propagator for TLE's. Inputs and outputs of this propagator are only suited for
   * NORAD two lines elements sets, since it uses estimations and mean values appropriate
   * for TLE's only.
   * </p>
   * <p>
   * Deep- or near- space propagator is selected internally according to NORAD recommendations
   * so that the user has not to worry about the used computation methods. One instance is created
   * for each TLE (this instance can only be get using {@link #selectExtrapolator(FieldTLE, CalculusFieldElement[])} method,
   * and can compute {@link PVCoordinates position and velocity coordinates} at any
   * time. Maximum accuracy is guaranteed in a 24h range period before and after the provided
   * TLE epoch (of course this accuracy is not really measurable nor predictable: according to
   * <a href="https://www.celestrak.com/">CelesTrak</a>, the precision is close to one kilometer
   * and error won't probably rise above 2 km).
   * </p>
   * <p>This implementation is largely inspired from the paper and source code <a
   * href="https://www.celestrak.com/publications/AIAA/2006-6753/">Revisiting Spacetrack
   * Report #3</a> and is fully compliant with its results and tests cases.</p>
   * @author Felix R. Hoots, Ronald L. Roehrich, December 1980 (original fortran)
   * @author David A. Vallado, Paul Crawford, Richard Hujsak, T.S. Kelso (C++ translation and improvements)
   * @author Fabien Maussion (java translation)
   * @author Thomas Paulet (field translation)
   * @since 11.0
   * @see FieldTLE
   * @param <T> type of the field elements
   */
  public abstract class FieldTLEPropagator<T extends CalculusFieldElement<T>> extends FieldAbstractAnalyticalPropagator<T> {
  
      // CHECKSTYLE: stop VisibilityModifier check
  
      /** Initial state. */
      protected FieldTLE<T> tle;
  
      /** UTC time scale. */
      protected final TimeScale utc;
  
      /** final RAAN. */
      protected T xnode;
  
      /** final semi major axis. */
      protected T a;
  
      /** final eccentricity. */
      protected T e;
  
      /** final inclination. */
      protected T i;
  
      /** final perigee argument. */
      protected T omega;
 
     /** L from SPTRCK #3. */
     protected T xl;
 
     /** original recovered semi major axis. */
     protected T a0dp;
 
     /** original recovered mean motion. */
     protected T xn0dp;
 
     /** cosinus original inclination. */
     protected T cosi0;
 
     /** cos io squared. */
     protected T theta2;
 
     /** sinus original inclination. */
     protected T sini0;
 
     /** common parameter for mean anomaly (M) computation. */
     protected T xmdot;
 
     /** common parameter for perigee argument (omega) computation. */
     protected T omgdot;
 
     /** common parameter for raan (OMEGA) computation. */
     protected T xnodot;
 
     /** original eccentricity squared. */
     protected T e0sq;
     /** 1 - e2. */
     protected T beta02;
 
     /** sqrt (1 - e2). */
     protected T beta0;
 
     /** perigee, expressed in KM and ALTITUDE. */
     protected T perige;
 
     /** eta squared. */
     protected T etasq;
 
     /** original eccentricity * eta. */
     protected T eeta;
 
     /** s* new value for the contant s. */
     protected T s4;
 
     /** tsi from SPTRCK #3. */
     protected T tsi;
 
     /** eta from SPTRCK #3. */
     protected T eta;
 
     /** coef for SGP C3 computation. */
     protected T coef;
 
     /** coef for SGP C5 computation. */
     protected T coef1;
 
     /** C1 from SPTRCK #3. */
     protected T c1;
 
     /** C2 from SPTRCK #3. */
     protected T c2;
 
     /** C4 from SPTRCK #3. */
     protected T c4;
 
     /** common parameter for raan (OMEGA) computation. */
     protected T xnodcf;
 
     /** 3/2 * C1. */
     protected T t2cof;
 
     // CHECKSTYLE: resume VisibilityModifier check
 
     /** TLE frame. */
     private final Frame teme;
 
     /** All TLEs and masses. */
     private TimeSpanMap<Pair<FieldTLE<T>, T>> tlesAndMasses;
 
     /** Protected constructor for derived classes.
      *
      * <p>This constructor uses the {@link DataContext#getDefault() default data context}.
      *
      * @param initialTLE the unique TLE to propagate
      * @param attitudeProvider provider for attitude computation
      * @param mass spacecraft mass (kg)
      * @param parameters SGP4 and SDP4 model parameters
      * @see #FieldTLEPropagator(FieldTLE, AttitudeProvider, CalculusFieldElement, Frame, CalculusFieldElement[])
      */
     @DefaultDataContext
     protected FieldTLEPropagator(final FieldTLE<T> initialTLE, final AttitudeProvider attitudeProvider, final T mass,
                                  final T[] parameters) {
         this(initialTLE, attitudeProvider, mass, DataContext.getDefault().getFrames().getTEME(), parameters);
     }
 
     /** Protected constructor for derived classes.
      * @param initialTLE the unique TLE to propagate
      * @param attitudeProvider provider for attitude computation
      * @param mass spacecraft mass (kg)
      * @param teme the TEME frame to use for propagation.
      * @param parameters SGP4 and SDP4 model parameters
      */
     protected FieldTLEPropagator(final FieldTLE<T> initialTLE, final AttitudeProvider attitudeProvider, final T mass,
                                  final Frame teme, final T[] parameters) {
         super(initialTLE.getE().getField(), attitudeProvider);
         setStartDate(initialTLE.getDate());
         this.utc       = initialTLE.getUtc();
         initializeTle(initialTLE);
         this.teme      = teme;
         this.tlesAndMasses      = new TimeSpanMap<>(new Pair<>(tle, mass));
 
         initializeCommons(parameters);
         sxpInitialize(parameters);
         // set the initial state
         final FieldOrbit<T> orbit = propagateOrbit(initialTLE.getDate(), parameters);
         final FieldAttitude<T> attitude = attitudeProvider.getAttitude(orbit, orbit.getDate(), orbit.getFrame());
         super.resetInitialState(new FieldSpacecraftState<>(orbit, attitude).withMass(mass));
     }
 
     /** Selects the extrapolator to use with the selected TLE.
      *
      * <p>This method uses the {@link DataContext#getDefault() default data context}.
      *
      * @param tle the TLE to propagate.
      * @param parameters SGP4 and SDP4 model parameters
      * @return the correct propagator.
      * @param <T> elements type
      * @see #selectExtrapolator(FieldTLE, Frame, CalculusFieldElement[])
      */
     @DefaultDataContext
     public static <T extends CalculusFieldElement<T>> FieldTLEPropagator<T> selectExtrapolator(final FieldTLE<T> tle, final T[] parameters) {
         return selectExtrapolator(tle, DataContext.getDefault().getFrames().getTEME(), parameters);
     }
 
     /** Selects the extrapolator to use with the selected TLE.
      *
      *<p>This method uses the {@link DataContext#getDefault() default data context}.
      *
      * @param tle the TLE to propagate.
      * @param teme TEME frame.
      * @param parameters SGP4 and SDP4 model parameters
      * @return the correct propagator.
      * @param <T> elements type
      */
     public static <T extends CalculusFieldElement<T>> FieldTLEPropagator<T> selectExtrapolator(final FieldTLE<T> tle, final Frame teme, final T[] parameters) {
         return selectExtrapolator(
                 tle,
                 FrameAlignedProvider.of(teme),
                 tle.getE().getField().getZero().newInstance(DEFAULT_MASS),
                 teme,
                 parameters);
     }
 
     /** Selects the extrapolator to use with the selected TLE.
      *
      * <p>This method uses the {@link DataContext#getDefault() default data context}.
      *
      * @param tle the TLE to propagate.
      * @param attitudeProvider provider for attitude computation
      * @param mass spacecraft mass (kg)
      * @param parameters SGP4 and SDP4 model parameters
      * @return the correct propagator.
      * @param <T> elements type
      * @see #selectExtrapolator(FieldTLE, AttitudeProvider, CalculusFieldElement, Frame, CalculusFieldElement[])
      */
     @DefaultDataContext
     public static <T extends CalculusFieldElement<T>> FieldTLEPropagator<T> selectExtrapolator(final FieldTLE<T> tle,
                                                    final AttitudeProvider attitudeProvider,
                                                    final T mass,
                                                    final T[] parameters) {
         return selectExtrapolator(tle, attitudeProvider, mass,
                 DataContext.getDefault().getFrames().getTEME(), parameters);
     }
 
     /** Selects the extrapolator to use with the selected TLE.
      *
      * @param tle the TLE to propagate.
      * @param attitudeProvider provider for attitude computation
      * @param mass spacecraft mass (kg)
      * @param teme the TEME frame to use for propagation.
      * @param parameters SGP4 and SDP4 model parameters
      * @return the correct propagator.
      * @param <T> elements type
      */
     public static <T extends CalculusFieldElement<T>> FieldTLEPropagator<T> selectExtrapolator(final FieldTLE<T> tle,
                                                    final AttitudeProvider attitudeProvider,
                                                    final T mass,
                                                    final Frame teme,
                                                    final T[] parameters) {
 
         final T a1 = tle.getMeanMotion().multiply(60.0).reciprocal().multiply(TLEConstants.XKE).pow(TLEConstants.TWO_THIRD);
         final T cosi0 = FastMath.cos(tle.getI());
         final T temp1 = cosi0.multiply(cosi0.multiply(3.0)).subtract(1.0).multiply(1.5 * TLEConstants.CK2);
         final T temp2 = tle.getE().multiply(tle.getE()).negate().add(1.0).pow(-1.5);
         final T temp = temp1.multiply(temp2);
         final T delta1 = temp.divide(a1.multiply(a1));
         final T a0 = a1.multiply(delta1.multiply(delta1.multiply(
                         delta1.multiply(134.0 / 81.0).add(1.0)).add(TLEConstants.ONE_THIRD)).negate().add(1.0));
         final T delta0 = temp.divide(a0.multiply(a0));
 
         // recover original mean motion :
         final T xn0dp = tle.getMeanMotion().multiply(60.0).divide(delta0.add(1.0));
 
         // Period >= 225 minutes is deep space
         if (MathUtils.TWO_PI / (xn0dp.multiply(TLEConstants.MINUTES_PER_DAY).getReal()) >= (1.0 / 6.4)) {
             return new FieldDeepSDP4<>(tle, attitudeProvider, mass, teme, parameters);
         } else {
             return new FieldSGP4<>(tle, attitudeProvider, mass, teme, parameters);
         }
     }
 
     /** Get the Earth gravity coefficient used for TLE propagation.
      * @return the Earth gravity coefficient.
      */
     public static double getMU() {
         return TLEConstants.MU;
     }
 
     /** Get the extrapolated position and velocity from an initial TLE.
      * @param date the final date
      * @param parameters values of the model
      * @return the final PVCoordinates
      */
     public FieldPVCoordinates<T> getPVCoordinates(final FieldAbsoluteDate<T> date, final T[] parameters) {
 
         sxpPropagate(date.durationFrom(tle.getDate()).divide(60.0), parameters);
 
         // Compute PV with previous calculated parameters
         return computePVCoordinates();
     }
 
     /** Computation of the first commons parameters.
      * @param parameters SGP4 and SDP4 model parameters
      */
     private void initializeCommons(final T[] parameters) {
 
         final T zero = tle.getDate().getField().getZero();
         final T bStar = parameters[0];
         final T a1 = tle.getMeanMotion().multiply(60.0).reciprocal().multiply(TLEConstants.XKE).pow(TLEConstants.TWO_THIRD);
         cosi0 = FastMath.cos(tle.getI());
         theta2 = cosi0.multiply(cosi0);
         final T x3thm1 = theta2.multiply(3.0).subtract(1.0);
         e0sq = tle.getE().square();
         beta02 = e0sq.negate().add(1.0);
         beta0 = FastMath.sqrt(beta02);
         final T tval = x3thm1.multiply(1.5 * TLEConstants.CK2).divide(beta0.multiply(beta02));
         final T delta1 = tval.divide(a1.multiply(a1));
         final T a0 = a1.multiply(delta1.multiply(
                      delta1.multiply(134.0 / 81.0).add(1.0).multiply(delta1).add(TLEConstants.ONE_THIRD)).negate().add(1.0));
         final T delta0 = tval.divide(a0.multiply(a0));
 
         // recover original mean motion and semi-major axis :
         xn0dp = tle.getMeanMotion().multiply(60.0).divide(delta0.add(1.0));
         a0dp = a0.divide(delta0.negate().add(1.0));
 
         // Values of s and qms2t :
         s4 = zero.newInstance(TLEConstants.S);  // unmodified value for s
         T q0ms24 = zero.newInstance(TLEConstants.QOMS2T); // unmodified value for q0ms2T
 
         perige = a0dp.multiply(tle.getE().negate().add(1.0)).subtract(TLEConstants.NORMALIZED_EQUATORIAL_RADIUS).multiply(
                                                                                                 TLEConstants.EARTH_RADIUS); // perige
 
         //  For perigee below 156 km, the values of s and qoms2t are changed :
         if (perige.getReal() < 156.0) {
             if (perige.getReal() <= 98.0) {
                 s4 = zero.newInstance(20.0);
             } else {
                 s4 = perige.subtract(78.0);
             }
             final T temp_val = s4.negate().add(120.0).multiply(TLEConstants.NORMALIZED_EQUATORIAL_RADIUS / TLEConstants.EARTH_RADIUS);
             final T temp_val_squared = temp_val.multiply(temp_val);
             q0ms24 = temp_val_squared.square();
             s4 = s4.divide(TLEConstants.EARTH_RADIUS).add(TLEConstants.NORMALIZED_EQUATORIAL_RADIUS); // new value for q0ms2T and s
         }
 
         final T pinv = a0dp.multiply(beta02).reciprocal();
         final T pinvsq = pinv.square();
         tsi = a0dp.subtract(s4).reciprocal();
         eta = a0dp.multiply(tle.getE()).multiply(tsi);
         etasq = eta.square();
         eeta = tle.getE().multiply(eta);
 
         final T psisq = etasq.negate().add(1.0).abs(); // abs because pow 3.5 needs positive value
         final T tsi_squared = tsi.multiply(tsi);
         coef = q0ms24.multiply(tsi_squared.square());
         coef1 = coef.divide(psisq.pow(3.5));
 
         // C2 and C1 coefficients computation :
         c2 = coef1.multiply(xn0dp).multiply(a0dp.multiply(
                            etasq.multiply(1.5).add(eeta.multiply(etasq.add(4.0))).add(1.0)).add(
                            tsi.divide(psisq).multiply(x3thm1).multiply(0.75 * TLEConstants.CK2).multiply(
                            etasq.multiply(etasq.add(8.0)).multiply(3.0).add(8.0))));
         c1 = bStar.multiply(c2);
         sini0 = FastMath.sin(tle.getI());
 
         final T x1mth2 = theta2.negate().add(1.0);
 
         // C4 coefficient computation :
         c4 = xn0dp.multiply(coef1).multiply(a0dp).multiply(2.0).multiply(beta02).multiply(
                            eta.multiply(etasq.multiply(0.5).add(2.0)).add(tle.getE().multiply(etasq.multiply(2.0).add(0.5))).subtract(
                            tsi.divide(a0dp.multiply(psisq)).multiply(2 * TLEConstants.CK2).multiply(
                            x3thm1.multiply(-3).multiply(etasq.multiply(eeta.multiply(-0.5).add(1.5)).add(eeta.multiply(-2.0)).add(1.0)).add(
                            x1mth2.multiply(0.75).multiply(etasq.multiply(2.0).subtract(eeta.multiply(etasq.add(1.0)))).multiply(FastMath.cos(tle.getPerigeeArgument().multiply(2.0)))))));
 
         final T theta4 = theta2.multiply(theta2);
         final T temp1  = pinvsq.multiply(xn0dp).multiply(3 * TLEConstants.CK2);
         final T temp2  = temp1.multiply(pinvsq).multiply(TLEConstants.CK2);
         final T temp3  = pinvsq.multiply(pinvsq).multiply(xn0dp).multiply(1.25 * TLEConstants.CK4);
 
         // atmospheric and gravitation coefs :(Mdf and OMEGAdf)
         xmdot = xn0dp.add(
                 temp1.multiply(0.5).multiply(beta0).multiply(x3thm1)).add(
                 temp2.multiply(0.0625).multiply(beta0).multiply(
                 theta2.multiply(78.0).negate().add(13.0).add(theta4.multiply(137.0))));
 
         final T x1m5th = theta2.multiply(5.0).negate().add(1.0);
 
         omgdot = temp1.multiply(-0.5).multiply(x1m5th).add(
                  temp2.multiply(0.0625).multiply(theta2.multiply(114.0).negate().add(
                  theta4.multiply(395.0)).add(7.0))).add(
                  temp3.multiply(theta2.multiply(36.0).negate().add(theta4.multiply(49.0)).add(3.0)));
 
         final T xhdot1 = temp1.negate().multiply(cosi0);
 
         xnodot = xhdot1.add(temp2.multiply(0.5).multiply(theta2.multiply(19.0).negate().add(4.0)).add(
                  temp3.multiply(2.0).multiply(theta2.multiply(7.0).negate().add(3.0))).multiply(cosi0));
         xnodcf = beta02.multiply(xhdot1).multiply(c1).multiply(3.5);
         t2cof = c1.multiply(1.5);
 
     }
 
     /** Retrieves the position and velocity.
      * @return the computed PVCoordinates.
      */
     private FieldPVCoordinates<T> computePVCoordinates() {
 
         final T zero = tle.getDate().getField().getZero();
         // Long period periodics
         final T axn = e.multiply(FastMath.cos(omega));
         T temp = a.multiply(e.multiply(e).negate().add(1.0)).reciprocal();
         final T xlcof = sini0.multiply(0.125 * TLEConstants.A3OVK2).multiply(
                              cosi0.multiply(5.0).add(3.0).divide(cosi0.add(1.0)));
         final T aycof = sini0.multiply(0.25 * TLEConstants.A3OVK2);
         final T xll   = temp.multiply(xlcof).multiply(axn);
         final T aynl  = temp.multiply(aycof);
         final T xlt   = xl.add(xll);
         final T ayn   = e.multiply(FastMath.sin(omega)).add(aynl);
         final T elsq  = axn.square().add(ayn.square());
         final T capu  = MathUtils.normalizeAngle(xlt.subtract(xnode), zero.getPi());
         T epw    = capu;
         T ecosE  = zero;
         T esinE  = zero;
         T sinEPW = zero;
         T cosEPW = zero;
 
         // Dundee changes:  items dependent on cosio get recomputed:
         final T cosi0Sq = cosi0.square();
         final T x3thm1  = cosi0Sq.multiply(3.0).subtract(1.0);
         final T x1mth2  = cosi0Sq.negate().add(1.0);
         final T x7thm1  = cosi0Sq.multiply(7.0).subtract(1.0);
 
         if (e.getReal() > (1 - 1e-6)) {
             throw new OrekitException(OrekitMessages.TOO_LARGE_ECCENTRICITY_FOR_PROPAGATION_MODEL, e);
         }
 
         // Solve Kepler's' Equation.
         final double newtonRaphsonEpsilon = 1e-12;
         for (int j = 0; j < 10; j++) {
 
             boolean doSecondOrderNewtonRaphson = true;
 
             sinEPW = FastMath.sin( epw);
             cosEPW = FastMath.cos( epw);
             ecosE  = axn.multiply(cosEPW).add(ayn.multiply(sinEPW));
             esinE  = axn.multiply(sinEPW).subtract(ayn.multiply(cosEPW));
             final T f = capu.subtract(epw).add(esinE);
             if (FastMath.abs(f.getReal()) < newtonRaphsonEpsilon) {
                 break;
             }
             final T fdot = ecosE.negate().add(1.0);
             T delta_epw = f.divide(fdot);
             if (j == 0) {
                 final T maxNewtonRaphson = e.abs().multiply(1.25);
                 doSecondOrderNewtonRaphson = false;
                 if (delta_epw.getReal() > maxNewtonRaphson.getReal()) {
                     delta_epw = maxNewtonRaphson;
                 } else if (delta_epw.getReal() < -maxNewtonRaphson.getReal()) {
                     delta_epw = maxNewtonRaphson.negate();
                 } else {
                     doSecondOrderNewtonRaphson = true;
                 }
             }
             if (doSecondOrderNewtonRaphson) {
                 delta_epw = f.divide(fdot.add(esinE.multiply(0.5).multiply(delta_epw)));
             }
             epw = epw.add(delta_epw);
         }
 
         // Short period preliminary quantities
         temp = elsq.negate().add(1.0);
         final T pl = a.multiply(temp);
         final T r  = a.multiply(ecosE.negate().add(1.0));
         T temp2 = a.divide(r);
         final T betal = FastMath.sqrt(temp);
         temp = esinE.divide(betal.add(1.0));
         final T cosu  = temp2.multiply(cosEPW.subtract(axn).add(ayn.multiply(temp)));
         final T sinu  = temp2.multiply(sinEPW.subtract(ayn).subtract(axn.multiply(temp)));
         final T u     = FastMath.atan2(sinu, cosu);
         final T sin2u = sinu.multiply(cosu).multiply(2.0);
         final T cos2u = cosu.multiply(cosu).multiply(2.0).subtract(1.0);
         final T temp1 = pl.reciprocal().multiply(TLEConstants.CK2);
         temp2         = temp1.divide(pl);
 
         // Update for short periodics
         final T rk = r.multiply(temp2.multiply(betal).multiply(x3thm1).multiply(-1.5).add(1.0)).add(
                      temp1.multiply(x1mth2).multiply(cos2u).multiply(0.5));
         final T uk = u.subtract(temp2.multiply(x7thm1).multiply(sin2u).multiply(0.25));
         final T xnodek = xnode.add(temp2.multiply(cosi0).multiply(sin2u).multiply(1.5));
         final T xinck = i.add(temp2.multiply(cosi0).multiply(sini0).multiply(cos2u).multiply(1.5));
 
         // Orientation vectors
         final T sinuk  = FastMath.sin(uk);
         final T cosuk  = FastMath.cos(uk);
         final T sinik  = FastMath.sin(xinck);
         final T cosik  = FastMath.cos(xinck);
         final T sinnok = FastMath.sin(xnodek);
         final T cosnok = FastMath.cos(xnodek);
         final T xmx    = sinnok.negate().multiply(cosik);
         final T xmy    = cosnok.multiply(cosik);
         final T ux     = xmx.multiply(sinuk).add(cosnok.multiply(cosuk));
         final T uy     = xmy.multiply(sinuk).add(sinnok.multiply(cosuk));
         final T uz     = sinik.multiply(sinuk);
 
         // Position and velocity
         final T cr = rk.multiply(1000 * TLEConstants.EARTH_RADIUS);
         final FieldVector3D<T> pos = new FieldVector3D<>(cr.multiply(ux), cr.multiply(uy), cr.multiply(uz));
 
         final T sqrtA  = FastMath.sqrt(a);
         final T rdot   = sqrtA.multiply(esinE.divide(r)).multiply(TLEConstants.XKE);
         final T rfdot  = FastMath.sqrt(pl).divide(r).multiply(TLEConstants.XKE);
         final T xn     = a.multiply(sqrtA).reciprocal().multiply(TLEConstants.XKE);
         final T rdotk  = rdot.subtract(xn.multiply(temp1).multiply(x1mth2).multiply(sin2u));
         final T rfdotk = rfdot.add(xn.multiply(temp1).multiply(x1mth2.multiply(cos2u).add(x3thm1.multiply(1.5))));
         final T vx     = xmx.multiply(cosuk).subtract(cosnok.multiply(sinuk));
         final T vy     = xmy.multiply(cosuk).subtract(sinnok.multiply(sinuk));
         final T vz     = sinik.multiply(cosuk);
 
         final double cv = 1000.0 * TLEConstants.EARTH_RADIUS / 60.0;
         final FieldVector3D<T> vel = new FieldVector3D<>(rdotk.multiply(ux).add(rfdotk.multiply(vx)).multiply(cv),
                                                           rdotk.multiply(uy).add(rfdotk.multiply(vy)).multiply(cv),
                                                           rdotk.multiply(uz).add(rfdotk.multiply(vz)).multiply(cv));
         return new FieldPVCoordinates<>(pos, vel);
 
     }
 
     /** {@inheritDoc} */
     @Override
     public List<ParameterDriver> getParametersDrivers() {
         return tle.getParametersDrivers();
     }
 
     /** Initialization proper to each propagator (SGP or SDP).
      * @param parameters model parameters
      */
     protected abstract void sxpInitialize(T[] parameters);
 
     /** Propagation proper to each propagator (SGP or SDP).
      * @param t the offset from initial epoch (min)
      * @param parameters model parameters
      */
     protected abstract void sxpPropagate(T t, T[] parameters);
 
     /** {@inheritDoc}
      * <p>
      * For TLE propagator, calling this method is only recommended
      * for covariance propagation when the new <code>state</code>
      * differs from the previous one by only adding the additional
      * state containing the derivatives.
      * </p>
      */
     public void resetInitialState(final FieldSpacecraftState<T> state) {
         super.resetInitialState(state);
         resetTle(state);
         tlesAndMasses = new TimeSpanMap<>(new Pair<>(tle, state.getMass()));
     }
 
     /** {@inheritDoc} */
     protected void resetIntermediateState(final FieldSpacecraftState<T> state, final boolean forward) {
         resetTle(state);
         final Pair<FieldTLE<T>, T> tleAndMass = new Pair<>(tle, state.getMass());
         if (forward) {
             tlesAndMasses.addValidAfter(tleAndMass, state.getDate().toAbsoluteDate(), false);
         } else {
             tlesAndMasses.addValidBefore(tleAndMass, state.getDate().toAbsoluteDate(), false);
         }
         stateChanged(state);
     }
 
     /** Reset internal TLE from a SpacecraftState.
      * @param state spacecraft state on which to base new TLE
      */
     private void resetTle(final FieldSpacecraftState<T> state) {
         final TleGenerationAlgorithm algorithm = TLEPropagator.getDefaultTleGenerationAlgorithm(utc, teme);
         final FieldTLE<T> newTle = algorithm.generate(state, tle);
         initializeTle(newTle);
     }
 
     /** Initialize internal TLE.
      * @param newTle tle to replace current one
      */
     private void initializeTle(final FieldTLE<T> newTle) {
         tle = newTle;
         final T[] parameters = tle.getParameters(tle.getDate().getField());
         initializeCommons(parameters);
         sxpInitialize(parameters);
     }
 
     /** {@inheritDoc} */
     protected T getMass(final FieldAbsoluteDate<T> date) {
         return tlesAndMasses.get(date.toAbsoluteDate()).getValue();
     }
 
     /** {@inheritDoc} */
     public FieldOrbit<T> propagateOrbit(final FieldAbsoluteDate<T> date, final T[] parameters) {
         final FieldTLE<T> closestTle = tlesAndMasses.get(date.toAbsoluteDate()).getKey();
         if (!tle.equals(closestTle)) {
             initializeTle(closestTle);
         }
         final T mu = date.getField().getZero().newInstance(TLEConstants.MU);
         return new FieldCartesianOrbit<>(getPVCoordinates(date, parameters), teme, date, mu);
     }
 
     /** Get the underlying TLE.
      * If there has been calls to #resetInitialState or #resetIntermediateState,
      * it will not be the same as given to the constructor.
      * @return underlying TLE
      */
     public FieldTLE<T> getTLE() {
         return tle;
     }
 
     /** {@inheritDoc} */
     public Frame getFrame() {
         return teme;
     }
 
 }