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    * contributor license agreements.  See the NOTICE file distributed with
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    * 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
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    *
    *   http://www.apache.org/licenses/LICENSE-2.0
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   * 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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   * See the License for the specific language governing permissions and
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  package org.orekit.forces.gravity;
  
  import java.util.Collections;
  import java.util.List;
  
  import org.hipparchus.CalculusFieldElement;
  import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
  import org.hipparchus.geometry.euclidean.threed.Vector3D;
  import org.hipparchus.util.FastMath;
  import org.orekit.forces.ForceModel;
  import org.orekit.frames.FieldStaticTransform;
  import org.orekit.frames.Frame;
  import org.orekit.frames.StaticTransform;
  import org.orekit.propagation.FieldSpacecraftState;
  import org.orekit.propagation.SpacecraftState;
  import org.orekit.utils.Constants;
  import org.orekit.utils.FieldPVCoordinates;
  import org.orekit.utils.PVCoordinates;
  import org.orekit.utils.ParameterDriver;
  
  /**
   * Lense-Thirring post-Newtonian correction force due to general relativity.
   * <p>
   * Lense-Thirring term causes a precession of the orbital plane at a rate of
   * the order of 0.8 mas per year (geostationary) to 180 mas per year (low orbit).
   * </p>
   * @see "Petit, G. and Luzum, B. (eds.), IERS Conventions (2010), Chapter 10,
   * General relativistic models for space-time coordinates and equations of motion (2010)"
   *
   * @author Bryan Cazabonne
   * @since 10.3
   */
  public class LenseThirringRelativity implements ForceModel {
  
      /** Intensity of the Earth's angular momentum per unit mass [m²/s]. */
      private static final double J = 9.8e8;
  
      /** Central attraction scaling factor.
       * <p>
       * We use a power of 2 to avoid numeric noise introduction
       * in the multiplications/divisions sequences.
       * </p>
       */
      private static final double MU_SCALE = FastMath.scalb(1.0, 32);
  
      /** Driver for gravitational parameter. */
      private final ParameterDriver gmParameterDriver;
  
      /** Central body frame. */
      private final Frame bodyFrame;
  
      /**
       * Constructor.
       * @param gm Earth's gravitational parameter.
       * @param bodyFrame central body frame
       */
      public LenseThirringRelativity(final double gm, final Frame bodyFrame) {
          gmParameterDriver = new ParameterDriver(NewtonianAttraction.CENTRAL_ATTRACTION_COEFFICIENT,
                                                  gm, MU_SCALE,
                                                  0.0, Double.POSITIVE_INFINITY);
          this.bodyFrame = bodyFrame;
      }
  
      /** {@inheritDoc} */
      @Override
      public boolean dependsOnPositionOnly() {
          return false;
      }
  
      /** {@inheritDoc} */
      @Override
      public Vector3D acceleration(final SpacecraftState s, final double[] parameters) {
  
          // Useful constant
          final double c2 = Constants.SPEED_OF_LIGHT * Constants.SPEED_OF_LIGHT;
  
          // Earth's gravitational parameter
          final double gm = parameters[0];
  
          // Satellite position and velocity with respect to the Earth
          final PVCoordinates pv = s.getPVCoordinates();
          final Vector3D p = pv.getPosition();
          final Vector3D v = pv.getVelocity();
 
         // Radius
         final double r  = p.getNorm();
         final double r2 = r * r;
 
         // Earth’s angular momentum per unit mass
         final StaticTransform t =
                 bodyFrame.getStaticTransformTo(s.getFrame(), s.getDate());
         final Vector3D  j = t.transformVector(Vector3D.PLUS_K).scalarMultiply(J);
 
         // Eq. 10.12
         return new Vector3D(3.0 * p.dotProduct(j) / r2,
                             p.crossProduct(v),
                             1.0,
                             v.crossProduct(j))
                             .scalarMultiply((2.0 * gm) / (r2 * r * c2));
     }
 
     /** {@inheritDoc} */
     @Override
     public <T extends CalculusFieldElement<T>> FieldVector3D<T> acceleration(final FieldSpacecraftState<T> s,
                                                                          final T[] parameters) {
 
         // Useful constant
         final double c2 = Constants.SPEED_OF_LIGHT * Constants.SPEED_OF_LIGHT;
 
         // Earth's gravitational parameter
         final T gm = parameters[0];
 
         // Satellite position and velocity with respect to the Earth
         final FieldPVCoordinates<T> pv = s.getPVCoordinates();
         final FieldVector3D<T> p = pv.getPosition();
         final FieldVector3D<T> v = pv.getVelocity();
 
         // Radius
         final T r  = p.getNorm();
         final T r2 = r.square();
 
         // Earth’s angular momentum per unit mass
         final FieldStaticTransform<T> t = bodyFrame.getStaticTransformTo(s.getFrame(), s.getDate());
         final FieldVector3D<T>        j = t.transformVector(Vector3D.PLUS_K).scalarMultiply(J);
 
         return new FieldVector3D<>(p.dotProduct(j).multiply(3.0).divide(r2),
                                    p.crossProduct(v),
                                    r.getField().getOne(),
                                    v.crossProduct(j))
                                    .scalarMultiply(gm.multiply(2.0).divide(r2.multiply(r).multiply(c2)));
     }
 
     /** {@inheritDoc} */
     @Override
     public List<ParameterDriver> getParametersDrivers() {
         return Collections.singletonList(gmParameterDriver);
     }
 
 }