//! Function to convert a Cartesian to a spherical orbital state.
basic_mathematics::Vector6d convertCartesianToSphericalOrbitalState(
const basic_mathematics::Vector6d& bodyFixedCartesianState )
{
basic_mathematics::Vector6d sphericalOrbitalState;
// Compute and set spherical position
Eigen::Vector3d sphericalPosition = coordinate_conversions::convertCartesianToSpherical(
bodyFixedCartesianState.segment( 0, 3 ) );
sphericalOrbitalState( radiusIndex ) = sphericalPosition( 0 );
sphericalOrbitalState( latitudeIndex ) = mathematical_constants::PI / 2.0 - sphericalPosition( 1 );
sphericalOrbitalState( longitudeIndex ) = sphericalPosition( 2 );
// Convert velocity to vertical frame.
Eigen::Vector3d verticalFrameVelocity =
reference_frames::getRotatingPlanetocentricToLocalVerticalFrameTransformationQuaternion(
sphericalOrbitalState( longitudeIndex ), sphericalOrbitalState( latitudeIndex ) ) *
bodyFixedCartesianState.segment( 3, 3 );
// Set velocity in spherical orbital state.
sphericalOrbitalState( speedIndex ) = verticalFrameVelocity.norm( );
sphericalOrbitalState( flightPathIndex ) = calculateFlightPathAngle( verticalFrameVelocity );
sphericalOrbitalState( headingAngleIndex ) = calculateHeadingAngle( verticalFrameVelocity );
return sphericalOrbitalState;
}
//! Transform a state (Cartesian position and velocity) from one frame to another.
basic_mathematics::Vector6d transformStateToFrame(
const basic_mathematics::Vector6d& stateInBaseFrame,
const Eigen::Quaterniond& rotationToFrame,
const Eigen::Matrix3d& rotationMatrixToFrameDerivative )
{
basic_mathematics::Vector6d stateInTargetFrame;
stateInTargetFrame.segment( 0, 3 ) =
rotationToFrame * stateInBaseFrame.segment( 0, 3 );
stateInTargetFrame.segment( 3, 3 ) =
rotationMatrixToFrameDerivative * stateInBaseFrame.segment( 0, 3 ) +
rotationToFrame * stateInBaseFrame.segment( 3, 3 );
return stateInTargetFrame;
}
//! Function to convert a spherical orbital to a Cartesian state.
basic_mathematics::Vector6d convertSphericalOrbitalToCartesianState(
const basic_mathematics::Vector6d& sphericalOrbitalState )
{
basic_mathematics::Vector6d cartesianState;
// Compute Cartesian position
Eigen::Vector3d sphericalPosition = sphericalOrbitalState.segment( 0, 3 );
sphericalPosition( 1 ) = mathematical_constants::PI / 2.0 - sphericalOrbitalState( 1 );
cartesianState.segment( 0, 3 ) = coordinate_conversions::convertSphericalToCartesian(
sphericalPosition );
// Check whether flight path angle and heading angle are valid (corresponding velocity components are zero otherwise)
bool isFlightPathAngleValid = ( sphericalOrbitalState( flightPathIndex ) == sphericalOrbitalState( flightPathIndex ) );
bool isHeadingAngleValid = ( sphericalOrbitalState( headingAngleIndex ) == sphericalOrbitalState( headingAngleIndex ) );
// Compute velocity in vertical frame.
Eigen::Vector3d velocityInVerticalFrame = Eigen::Vector3d::Zero( );
if( isFlightPathAngleValid && isHeadingAngleValid )
{
velocityInVerticalFrame( 0 ) = sphericalOrbitalState( speedIndex ) *
std::cos( sphericalOrbitalState( flightPathIndex ) ) *
std::cos( sphericalOrbitalState( headingAngleIndex ) );
velocityInVerticalFrame( 1 ) = sphericalOrbitalState( speedIndex ) *
std::cos( sphericalOrbitalState( flightPathIndex ) ) *
std::sin( sphericalOrbitalState( headingAngleIndex ) );
}
if( isFlightPathAngleValid )
{
velocityInVerticalFrame( 2 ) = -sphericalOrbitalState( speedIndex ) *
std::sin( sphericalOrbitalState( flightPathIndex ) );
}
// Set velocity in body-fixed frame.
cartesianState.segment( 3, 3 ) = reference_frames::getLocalVerticalToRotatingPlanetocentricFrameTransformationQuaternion(
sphericalOrbitalState( longitudeIndex ), sphericalOrbitalState( latitudeIndex ) ) * velocityInVerticalFrame;
return cartesianState;
}
int main( )
{
// Set directory where output files will be stored. By default, this is your project
// root-directory.
const std::string outputDirectory = basic_input_output::getApplicationRootPath( ) + "/";
// Set bounds for the departure dates from Earth to the target planet, its step-size and number
// of steps. Notice how an integer is cast into a double.
const double lowerBoundDepartureDate = 8400.0;
const double upperBoundDepartureDate = 9860.0;
const unsigned int numberOfStepsDepartureDate = 1461;
const double stepSizeDepartureDate = ( upperBoundDepartureDate - lowerBoundDepartureDate ) /
static_cast< double >( numberOfStepsDepartureDate - 1 );
// Set bounds for the transfer time from Earth to the target planet, its step-size and number
// of steps.
const double lowerBoundTransferTime = 100.0;
const double upperBoundTransferTime = 400.0;
const unsigned int numberOfStepsTransferTime = 301;
const double stepSizeTransferTime = ( upperBoundTransferTime - lowerBoundTransferTime ) /
static_cast< double >( numberOfStepsTransferTime - 1 );
// Fill the departure dates vector and the transfer times vector.
// Note that you can use the variable "counter" in both for-loops, since it is in local scope.
Eigen::VectorXd departureDates( numberOfStepsDepartureDate ),
transferTimes( numberOfStepsTransferTime );
for ( unsigned int counter = 0; counter < numberOfStepsDepartureDate; counter++ )
{
departureDates( counter ) = lowerBoundDepartureDate + counter * stepSizeDepartureDate;
}
for ( unsigned int counter = 0; counter < numberOfStepsTransferTime; counter++ )
{
transferTimes( counter ) = lowerBoundTransferTime + counter * stepSizeTransferTime;
}
// Initialize a matrix that will keep track of the deltaVs.
Eigen::MatrixXd deltaVs( numberOfStepsTransferTime, numberOfStepsDepartureDate );
// Start the grid search.
// Loop through all the transfer times.
// Note in this case that because there are nested loops, the counter variables must be named
// differently!
for ( unsigned int counter1 = 0; counter1 < numberOfStepsTransferTime; counter1++ )
{
// Set the transfer time.
const double transferTimeInDays = transferTimes( counter1 );
// Loop through all the departure dates.
for( unsigned int counter2 = 0; counter2 < numberOfStepsDepartureDate; counter2++ )
{
// Set the departure date.
const double departureDateInMJD2000 = departureDates( counter2 );
// Calculate the arrival date.
const double arrivalDateInMJD2000 = departureDateInMJD2000 + transferTimeInDays;
// Obtain Keplerian elements of the planets.
const basic_mathematics::Vector6d earthKeplerianElements =
ephemeris::getKeplerianElementsOfPlanet(
mission_definitions::ephemerisEarth, departureDateInMJD2000 );
const basic_mathematics::Vector6d targetKeplerianElements
= ephemeris::getKeplerianElementsOfPlanet(
mission_definitions::ephemerisTarget, arrivalDateInMJD2000 );
// Convert Keplerian elements into Cartesian position and velocity of the planets.
const basic_mathematics::Vector6d earthCartesianElements =
orbital_element_conversions::convertKeplerianToCartesianElements(
earthKeplerianElements, mission_definitions::gravitationalParameterSun );
const basic_mathematics::Vector6d targetCartesianElements =
orbital_element_conversions::convertKeplerianToCartesianElements(
targetKeplerianElements, mission_definitions::gravitationalParameterSun );
// Split the cartesian elements into position and velocity.
const Eigen::Vector3d earthPosition = earthCartesianElements.segment( 0, 3 );
const Eigen::Vector3d earthVelocity = earthCartesianElements.segment( 3, 3 );
const Eigen::Vector3d targetPosition = targetCartesianElements.segment( 0, 3 );
const Eigen::Vector3d targetVelocity = targetCartesianElements.segment( 3, 3 );
// Convert transfer time to seconds.
const double transferTime = tudat::
unit_conversions::convertJulianDaysToSeconds( transferTimeInDays );
// Initialize the vectors that will contain the spacecraft velocities.
Eigen::Vector3d velocityAtEarth, velocityAtTarget;
// Compute these velocities using the Lambert targeter.
mission_segments::solveLambertProblemIzzo(
earthPosition, targetPosition, transferTime,
mission_definitions::gravitationalParameterSun,
velocityAtEarth, velocityAtTarget );
// Compute the velocity increments at Earth and the target.
const Eigen::Vector3d velocityIncrementAtEarth = velocityAtEarth - earthVelocity;
const Eigen::Vector3d velocityIncrementAtTarget = velocityAtTarget - targetVelocity;
// Compute the excess velocities at Earth and the target.
const double excessVelocityAtEarth = velocityIncrementAtEarth.norm( );
const double excessVelocityAtTarget = velocityIncrementAtTarget.norm( );
// Compute the deltaV for the escape and capture maneuvers.
const double deltaVatEarth = mission_segments::computeEscapeOrCaptureDeltaV(
mission_definitions::gravitationalParameterEarth,
mission_definitions::parkingOrbitSemiMajorAxis,
mission_definitions::parkingOrbitEccentricity, excessVelocityAtEarth );
const double deltaVAtTarget = mission_segments::computeEscapeOrCaptureDeltaV(
mission_definitions::gravitationalParameterTarget,
mission_definitions::captureOrbitSemiMajorAxis,
mission_definitions::captureOrbitEccentricity, excessVelocityAtTarget );
// Compute the total deltaV and store it in the matrix.
deltaVs( counter1, counter2 ) = deltaVatEarth + deltaVAtTarget;
}
}
// Write the results to comma separated files. These are ready to be read in by MATLAB using
// the csvread() function and the matrix can be plotted directly as a mesh.
// Set output format for matrix output.
Eigen::IOFormat csvFormat( 15, 0, ", ", "\n" );
// Set absolute path to file containing deltaVs.
const std::string deltaVOutputFileAbsolutePath = outputDirectory + "DeltaVsPartD.csv";
// Export the deltaV matrix.
std::ofstream exportFile1( deltaVOutputFileAbsolutePath.c_str( ) );
exportFile1 << deltaVs.format( csvFormat );
exportFile1.close( );
// Set absolute path to file containing departure dates.
const std::string departureDateOutputFileAbsolutePath
= outputDirectory + "DepartureDatesPartD.csv";
// Export the departure dates vector.
std::ofstream exportFile2( departureDateOutputFileAbsolutePath.c_str( ) );
exportFile2.precision( 15 );
exportFile2 << departureDates;
exportFile2.close( );
// Set absolute path to file containing transfer times.
const std::string transferTimesOutputFileAbsolutePath
= outputDirectory + "TransferTimesPartD.csv";
// Export the transfer times vector.
std::ofstream exportFile3( transferTimesOutputFileAbsolutePath.c_str( ) );
exportFile3.precision( 15 );
exportFile3 << transferTimes;
exportFile3.close( );
return 0;
}