The next tutorials detail some elementary usages of the maneuvers. Both simple impulsive maneuvers and more complex continuous thrust maneuvers are presented.
Impulsive maneuvers are very simple discrete changes to the velocity of a spacecraft. They are mainly used in two cases:
This tutorial shows how to implement a series of maneuvers to change progressively the inclination of an orbit.
Let’s set up an initial state as:
final Frame eme2000 = FramesFactory.getEME2000();
final Orbit initialOrbit =
new KeplerianOrbit(8000000.0, 0.01,
FastMath.toRadians(50.0), // ← this is initial inclination
FastMath.toRadians(140.0),
FastMath.toRadians(12.0),
FastMath.toRadians(-60.0), PositionAngle.MEAN,
eme2000,
new AbsoluteDate(new DateComponents(2008, 6, 23),
new TimeComponents(14, 0, 0),
TimeScalesFactory.getUTC()),
Constants.EIGEN5C_EARTH_MU);
The maneuver will be defined in spacecraft frame. We need to ensure the Z axis is aligned with orbital momentum, so we select an attitude aligned with LVLH Local Orbital frame
final AttitudeProvider attitudeProvider = new LofOffset(eme2000, LOFType.LVLH);
We want to perform a series of 3 inclination reduction maneuvers. As they modify only inclination, they must occur at node, but not all nodes are suitable, we want ascending nodes, with a ΔV along -Z. The maneuvers are triggered when Action.STOP events occur (and are filtered out)
final NodeDetector ascendingNodeStopper =
new NodeDetector(FramesFactory.getEME2000()).
withMaxCheck(300.0).
withThreshold(1.0e-6).
withHandler(new StopOnIncreasing<>());
We allow only maneuvers on the first 3 orbits
final AbsoluteDate lastAllowedDate =
initialOrbit.getDate().shiftedBy(3 * initialOrbit.getKeplerianPeriod());
final EnablingPredicate<EventDetector> predicate =
(state, detector, g) -> state.getDate().isBefore(lastAllowedDate);
final EventDetector trigger =
new EventEnablingPredicateFilter<>(ascendingNodeStopper, predicate);
Create the maneuver, using ascending node detector as a trigger
final ImpulseManeuver<EventDetector> maneuver =
new ImpulseManeuver<>(trigger,
new Vector3D(0.0, 0.0, -122.25), // ← 122.25 m/s along -Z
350.0);
Wrap-up everything in a propagator. Note that ImpulseManeuver is a event detector, not a force model! This allows it to be used for all propagators, including analytical ones like the Keplerian propagator used here
final KeplerianPropagator propagator = new KeplerianPropagator(initialOrbit, attitudeProvider); propagator.addEventDetector(maneuver);
Progress monitoring
propagator.getMultiplexer().add(900.0, (state, isLast) -> {
final Vector3D pos = state.getPVCoordinates(eme2000).getPosition();
System.out.format(Locale.US, "%s %s hemisphere inclination = %5.3f%n",
state.getDate(),
pos.getZ() > 0 ? "Northern" : "Southern",
FastMath.toDegrees(state.getOrbit().getI()));
});
Run simulation
propagator.propagate(initialOrbit.getDate().shiftedBy(5 * initialOrbit.getKeplerianPeriod()));
The printed result is shown below. We see that inclination remains constant as we cross descending nodes (i.e. switch from Northern to Southern hemisphere), and changes as we cross the first three ascending nodes
2008-06-23T14:00:00.000 Northern hemisphere inclination = 50.000 2008-06-23T14:15:00.000 Northern hemisphere inclination = 50.000 2008-06-23T14:30:00.000 Northern hemisphere inclination = 50.000 2008-06-23T14:45:00.000 Southern hemisphere inclination = 50.000 2008-06-23T15:00:00.000 Southern hemisphere inclination = 50.000 2008-06-23T15:15:00.000 Southern hemisphere inclination = 50.000 2008-06-23T15:30:00.000 Southern hemisphere inclination = 50.000 2008-06-23T15:45:00.000 Northern hemisphere inclination = 49.000 2008-06-23T16:00:00.000 Northern hemisphere inclination = 49.000 2008-06-23T16:15:00.000 Northern hemisphere inclination = 49.000 2008-06-23T16:30:00.000 Northern hemisphere inclination = 49.000 2008-06-23T16:45:00.000 Southern hemisphere inclination = 49.000 2008-06-23T17:00:00.000 Southern hemisphere inclination = 49.000 2008-06-23T17:15:00.000 Southern hemisphere inclination = 49.000 2008-06-23T17:30:00.000 Southern hemisphere inclination = 49.000 2008-06-23T17:45:00.000 Northern hemisphere inclination = 48.001 2008-06-23T18:00:00.000 Northern hemisphere inclination = 48.001 2008-06-23T18:15:00.000 Northern hemisphere inclination = 48.001 2008-06-23T18:30:00.000 Northern hemisphere inclination = 48.001 2008-06-23T18:45:00.000 Southern hemisphere inclination = 48.001 2008-06-23T19:00:00.000 Southern hemisphere inclination = 48.001 2008-06-23T19:15:00.000 Southern hemisphere inclination = 48.001 2008-06-23T19:30:00.000 Southern hemisphere inclination = 48.001 2008-06-23T19:45:00.000 Northern hemisphere inclination = 47.001 2008-06-23T20:00:00.000 Northern hemisphere inclination = 47.001 2008-06-23T20:15:00.000 Northern hemisphere inclination = 47.001 2008-06-23T20:30:00.000 Southern hemisphere inclination = 47.001 2008-06-23T20:45:00.000 Southern hemisphere inclination = 47.001 2008-06-23T21:00:00.000 Southern hemisphere inclination = 47.001 2008-06-23T21:15:00.000 Southern hemisphere inclination = 47.001 2008-06-23T21:30:00.000 Northern hemisphere inclination = 47.001 2008-06-23T21:45:00.000 Northern hemisphere inclination = 47.001 2008-06-23T22:00:00.000 Northern hemisphere inclination = 47.001 2008-06-23T22:15:00.000 Northern hemisphere inclination = 47.001 2008-06-23T22:30:00.000 Southern hemisphere inclination = 47.001 2008-06-23T22:45:00.000 Southern hemisphere inclination = 47.001 2008-06-23T23:00:00.000 Southern hemisphere inclination = 47.001 2008-06-23T23:15:00.000 Southern hemisphere inclination = 47.001 2008-06-23T23:30:00.000 Northern hemisphere inclination = 47.001 2008-06-23T23:45:00.000 Northern hemisphere inclination = 47.001
The complete code for this example can be found in the source tree of the tutorials, in file src/main/java/org/orekit/tutorials/maneuvers/ImpulseAtNode.java.
Continuous maneuvers are realistic models that take into account maneuver duration, attitude change during maneuver and mass depletion. They can only be used with integration-based propagators.
This tutorial shows how to implement an apogee maneuver, using either the attitude set up at propagator level itself or overriding it for only the maneuver acceleration direction computation. We use only date-based triggers and constant thrust propulsion system, but it is possible to use different ones. As an example, we could replace the BasicConstantThrustPropulsionModel with ScaledConstantThrustPropulsionModel and to take into account some calibration factors (or estimate these factors if instead of using this model in a simulation we use it in an orbit determination and configure these scaling factors as estimated). We could also replace the date-based triggers by event-based triggers, which can model multi-burn maneuvers.
Let’s set up an initial state with a GTO orbit and a 2500kg spacecraft:
final Frame eme2000 = FramesFactory.getEME2000();
final AbsoluteDate date = new AbsoluteDate(new DateComponents(2004, 01, 01),
new TimeComponents(23, 30, 00.000),
TimeScalesFactory.getUTC());
final Orbit orbit =
new KeplerianOrbit(24396159, 0.72831215, FastMath.toRadians(7),
FastMath.toRadians(180), FastMath.toRadians(261),
FastMath.toRadians(0), PositionAngle.TRUE,
eme2000, date,
Constants.EIGEN5C_EARTH_MU);
final SpacecraftState initialState = new SpacecraftState(orbit, 2500.0);
Prepare propagator, using an adaptive stepsize integrator. The propagator will use an attitude mode aligned with VNC, i.e. its X axis is always along orbital velocity
final OrbitType orbitType = OrbitType.EQUINOCTIAL;
final double[][] tol = NumericalPropagator.tolerances(1.0, orbit, orbitType);
final AdaptiveStepsizeIntegrator integrator =
new DormandPrince853Integrator(0.001, 1000, tol[0], tol[1]);
integrator.setInitialStepSize(60);
final NumericalPropagator propagator = new NumericalPropagator(integrator);
propagator.setOrbitType(orbitType);
propagator.setInitialState(initialState);
propagator.setAttitudeProvider(new LofOffset(eme2000, LOFType.VNC));
At first, we want to compute the maneuver as an inertial one, so we cannot rely on the attitude mode configured above, we need an attitude overriding law with the X axis pointing towards a specific direction
final Vector3D direction = new Vector3D(FastMath.toRadians(-7.4978),
FastMath.toRadians(351));
final AttitudeProvider attitudeOverride =
new InertialProvider(new Rotation(direction, Vector3D.PLUS_I),
eme2000);
Maneuver will start at a known date and stop after a known duration
final AbsoluteDate firingDate = new AbsoluteDate(new DateComponents(2004, 1, 2), new TimeComponents(4, 15, 34.080), TimeScalesFactory.getUTC()); final double duration = 3653.99; final ManeuverTriggers triggers = new DateBasedManeuverTriggers(firingDate, duration);
Maneuver has constant thrust
final double thrust = 420; final double isp = 318; final PropulsionModel propulsionModel = new BasicConstantThrustPropulsionModel(thrust, isp, Vector3D.PLUS_I, “apogee-engine”);
Build maneuver and add it to the propagator as a new force model
propagator.addForceModel(new Maneuver(attitudeOverride, triggers, propulsionModel));
Progress monitoring
propagator.getMultiplexer().add(120.0, (state, isLast) ->
System.out.format(Locale.US, "%s a = %12.3f m, e = %11.9f, m = %8.3f kg%n",
state.getDate(), state.getA(), state.getE(), state.getMass())
);
Propagate orbit, including maneuver
propagator.propagate(fireDate.shiftedBy(-900), fireDate.shiftedBy(duration + 900));
The printed result is shown below. We see that semi-major axis, eccentricity and inclination are constant before the maneuver, they change continuously during the maneuver, and become constant again after maneuver
2004-01-02T04:00:34.080 a = 24396159.000 m, e = 0.728312150, m = 2500.000 kg 2004-01-02T04:02:34.080 a = 24396159.000 m, e = 0.728312150, m = 2500.000 kg 2004-01-02T04:04:34.080 a = 24396159.000 m, e = 0.728312150, m = 2500.000 kg 2004-01-02T04:06:34.080 a = 24396159.000 m, e = 0.728312150, m = 2500.000 kg 2004-01-02T04:08:34.080 a = 24396159.000 m, e = 0.728312150, m = 2500.000 kg 2004-01-02T04:10:34.080 a = 24396159.000 m, e = 0.728312150, m = 2500.000 kg 2004-01-02T04:12:34.080 a = 24396159.000 m, e = 0.728312150, m = 2500.000 kg 2004-01-02T04:14:34.080 a = 24396159.000 m, e = 0.728312150, m = 2500.000 kg 2004-01-02T04:16:34.080 a = 24442112.400 m, e = 0.725043403, m = 2491.919 kg 2004-01-02T04:18:34.080 a = 24536037.252 m, e = 0.718404119, m = 2475.758 kg 2004-01-02T04:20:34.080 a = 24632720.409 m, e = 0.711627339, m = 2459.596 kg 2004-01-02T04:22:34.080 a = 24732246.157 m, e = 0.704710905, m = 2443.435 kg 2004-01-02T04:24:34.080 a = 24834702.625 m, e = 0.697652633, m = 2427.273 kg 2004-01-02T04:26:34.080 a = 24940182.000 m, e = 0.690450311, m = 2411.112 kg 2004-01-02T04:28:34.080 a = 25048780.751 m, e = 0.683101699, m = 2394.950 kg 2004-01-02T04:30:34.080 a = 25160599.875 m, e = 0.675604529, m = 2378.788 kg 2004-01-02T04:32:34.080 a = 25275745.160 m, e = 0.667956507, m = 2362.627 kg 2004-01-02T04:34:34.080 a = 25394327.460 m, e = 0.660155308, m = 2346.465 kg 2004-01-02T04:36:34.080 a = 25516463.000 m, e = 0.652198582, m = 2330.304 kg 2004-01-02T04:38:34.080 a = 25642273.694 m, e = 0.644083951, m = 2314.142 kg 2004-01-02T04:40:34.080 a = 25771887.491 m, e = 0.635809009, m = 2297.981 kg 2004-01-02T04:42:34.080 a = 25905438.748 m, e = 0.627371325, m = 2281.819 kg 2004-01-02T04:44:34.080 a = 26043068.626 m, e = 0.618768440, m = 2265.658 kg 2004-01-02T04:46:34.080 a = 26184925.522 m, e = 0.609997872, m = 2249.496 kg 2004-01-02T04:48:34.080 a = 26331165.531 m, e = 0.601057114, m = 2233.335 kg 2004-01-02T04:50:34.080 a = 26481952.946 m, e = 0.591943638, m = 2217.173 kg 2004-01-02T04:52:34.080 a = 26637460.795 m, e = 0.582654892, m = 2201.012 kg 2004-01-02T04:54:34.080 a = 26797871.426 m, e = 0.573188310, m = 2184.850 kg 2004-01-02T04:56:34.080 a = 26963377.135 m, e = 0.563541304, m = 2168.688 kg 2004-01-02T04:58:34.080 a = 27134180.848 m, e = 0.553711279, m = 2152.527 kg 2004-01-02T05:00:34.080 a = 27310496.862 m, e = 0.543695627, m = 2136.365 kg 2004-01-02T05:02:34.080 a = 27492551.643 m, e = 0.533491736, m = 2120.204 kg 2004-01-02T05:04:34.080 a = 27680584.703 m, e = 0.523096997, m = 2104.042 kg 2004-01-02T05:06:34.080 a = 27874849.544 m, e = 0.512508806, m = 2087.881 kg 2004-01-02T05:08:34.080 a = 28075614.691 m, e = 0.501724576, m = 2071.719 kg 2004-01-02T05:10:34.080 a = 28283164.817 m, e = 0.490741747, m = 2055.558 kg 2004-01-02T05:12:34.080 a = 28497801.970 m, e = 0.479557796, m = 2039.396 kg 2004-01-02T05:14:34.080 a = 28719846.917 m, e = 0.468170253, m = 2023.235 kg 2004-01-02T05:16:34.080 a = 28937941.941 m, e = 0.457162297, m = 2007.882 kg 2004-01-02T05:18:34.080 a = 28937941.941 m, e = 0.457162297, m = 2007.882 kg 2004-01-02T05:20:34.080 a = 28937941.941 m, e = 0.457162297, m = 2007.882 kg 2004-01-02T05:22:34.080 a = 28937941.941 m, e = 0.457162297, m = 2007.882 kg 2004-01-02T05:24:34.080 a = 28937941.941 m, e = 0.457162297, m = 2007.882 kg 2004-01-02T05:26:34.080 a = 28937941.941 m, e = 0.457162297, m = 2007.882 kg 2004-01-02T05:28:34.080 a = 28937941.941 m, e = 0.457162297, m = 2007.882 kg 2004-01-02T05:30:34.080 a = 28937941.941 m, e = 0.457162297, m = 2007.882 kg
If instead of overriding the attitude we want to use the attitude configured in the propagator (which here is VNC-aligned), then we simply set the attitude overriding parameter to null when building the maneuver:
propagator.addForceModel(new Maneuver(null, triggers, propulsionModel));
The results with this configuration would become:
2004-01-02T04:00:34.080 a = 24396159.000 m, e = 0.728312150, m = 2500.000 kg 2004-01-02T04:02:34.080 a = 24396159.000 m, e = 0.728312150, m = 2500.000 kg 2004-01-02T04:04:34.080 a = 24396159.000 m, e = 0.728312150, m = 2500.000 kg 2004-01-02T04:06:34.080 a = 24396159.000 m, e = 0.728312150, m = 2500.000 kg 2004-01-02T04:08:34.080 a = 24396159.000 m, e = 0.728312150, m = 2500.000 kg 2004-01-02T04:10:34.080 a = 24396159.000 m, e = 0.728312150, m = 2500.000 kg 2004-01-02T04:12:34.080 a = 24396159.000 m, e = 0.728312150, m = 2500.000 kg 2004-01-02T04:14:34.080 a = 24396159.000 m, e = 0.728312150, m = 2500.000 kg 2004-01-02T04:16:34.080 a = 24445841.001 m, e = 0.724984968, m = 2491.919 kg 2004-01-02T04:18:34.080 a = 24547017.613 m, e = 0.718218653, m = 2475.758 kg 2004-01-02T04:20:34.080 a = 24650693.763 m, e = 0.711301532, m = 2459.596 kg 2004-01-02T04:22:34.080 a = 24756972.407 m, e = 0.704231757, m = 2443.435 kg 2004-01-02T04:24:34.080 a = 24865960.944 m, e = 0.697007471, m = 2427.273 kg 2004-01-02T04:26:34.080 a = 24977771.472 m, e = 0.689626812, m = 2411.112 kg 2004-01-02T04:28:34.080 a = 25092521.078 m, e = 0.682087911, m = 2394.950 kg 2004-01-02T04:30:34.080 a = 25210332.139 m, e = 0.674388891, m = 2378.788 kg 2004-01-02T04:32:34.080 a = 25331332.649 m, e = 0.666527867, m = 2362.627 kg 2004-01-02T04:34:34.080 a = 25455656.575 m, e = 0.658502951, m = 2346.465 kg 2004-01-02T04:36:34.080 a = 25583444.233 m, e = 0.650312244, m = 2330.304 kg 2004-01-02T04:38:34.080 a = 25714842.703 m, e = 0.641953845, m = 2314.142 kg 2004-01-02T04:40:34.080 a = 25850006.270 m, e = 0.633425850, m = 2297.981 kg 2004-01-02T04:42:34.080 a = 25989096.901 m, e = 0.624726354, m = 2281.819 kg 2004-01-02T04:44:34.080 a = 26132284.765 m, e = 0.615853455, m = 2265.658 kg 2004-01-02T04:46:34.080 a = 26279748.789 m, e = 0.606805258, m = 2249.496 kg 2004-01-02T04:48:34.080 a = 26431677.269 m, e = 0.597579879, m = 2233.335 kg 2004-01-02T04:50:34.080 a = 26588268.522 m, e = 0.588175453, m = 2217.173 kg 2004-01-02T04:52:34.080 a = 26749731.602 m, e = 0.578590139, m = 2201.012 kg 2004-01-02T04:54:34.080 a = 26916287.072 m, e = 0.568822132, m = 2184.850 kg 2004-01-02T04:56:34.080 a = 27088167.851 m, e = 0.558869672, m = 2168.688 kg 2004-01-02T04:58:34.080 a = 27265620.125 m, e = 0.548731056, m = 2152.527 kg 2004-01-02T05:00:34.080 a = 27448904.347 m, e = 0.538404659, m = 2136.365 kg 2004-01-02T05:02:34.080 a = 27638296.331 m, e = 0.527888947, m = 2120.204 kg 2004-01-02T05:04:34.080 a = 27834088.441 m, e = 0.517182503, m = 2104.042 kg 2004-01-02T05:06:34.080 a = 28036590.891 m, e = 0.506284055, m = 2087.881 kg 2004-01-02T05:08:34.080 a = 28246133.176 m, e = 0.495192508, m = 2071.719 kg 2004-01-02T05:10:34.080 a = 28463065.636 m, e = 0.483906983, m = 2055.558 kg 2004-01-02T05:12:34.080 a = 28687761.178 m, e = 0.472426869, m = 2039.396 kg 2004-01-02T05:14:34.080 a = 28920617.165 m, e = 0.460751878, m = 2023.235 kg 2004-01-02T05:16:34.080 a = 29149754.286 m, e = 0.449481220, m = 2007.882 kg 2004-01-02T05:18:34.080 a = 29149754.286 m, e = 0.449481220, m = 2007.882 kg 2004-01-02T05:20:34.080 a = 29149754.286 m, e = 0.449481220, m = 2007.882 kg 2004-01-02T05:22:34.080 a = 29149754.286 m, e = 0.449481220, m = 2007.882 kg 2004-01-02T05:24:34.080 a = 29149754.286 m, e = 0.449481220, m = 2007.882 kg 2004-01-02T05:26:34.080 a = 29149754.286 m, e = 0.449481220, m = 2007.882 kg 2004-01-02T05:28:34.080 a = 29149754.286 m, e = 0.449481220, m = 2007.882 kg 2004-01-02T05:30:34.080 a = 29149754.286 m, e = 0.449481220, m = 2007.882 kg
As expected, we see that for the same fuel consumption, semi-major axis increases more and eccentricity decreases more when the attitude is always kept aligned with velocity than when attitude is inertial.
The complete code for this example can be found in the source tree of the tutorials, in file src/main/java/org/orekit/tutorials/maneuvers/ApogeeManeuver.java.