Integrators¶

Integrators advance spacecraft state through time under configured force models. Both community and Pro integrators share a common interface and produce dense-output records.

IIntegrator Interface¶

Method	Description
`Initialize(StateVector)`	Set initial conditions and force model context
`IntegrateSegment(pos, vel, baseEpoch, duration, eventDetectors)`	Advance state, returning `IntegrationResult`

IntegrationResult contains the completed PropagationSegment and optional event information if a detector triggered during the segment.

AcceptedStep¶

Both integrators record AcceptedStep entries containing position, velocity, and acceleration at the start and end of each step. These records enable cubic Hermite interpolation for dense output between steps.

VVIntegrator¶

VVIntegrator is the community fixed-step symplectic integrator using the Velocity-Verlet scheme.

Parameter	Type	Description
`stepSize`	`double`	Fixed time step in seconds

Property	Description
`StepSize`	The configured step size (s)

Symplectic: conserves energy over long durations for conservative systems.
Event detection occurs at step boundaries only (no sub-step refinement).
Suitable for quick analyses where adaptive accuracy is not required.

var integrator = new VVIntegrator(stepSize: 10.0);

RK78Integrator¶

Pro

RK78Integrator is a Pro feature. The community edition provides VVIntegrator.

RK78Integrator implements the Prince-Dormand 7(8) method: a 13-stage, 8th-order integrator with an embedded 7th-order error estimate for adaptive step control.

Adaptive Constructor¶

Parameter	Type	Default	Description
`absoluteTolerance`	`double`	`1e-9`	Absolute error tolerance
`relativeTolerance`	`double`	`1e-9`	Relative error tolerance
`initialStepSize`	`double`	`60.0`	Initial step size (s)
`minStepSize`	`double`	`1e-6`	Minimum allowed step size (s)
`maxStepSize`	`double`	`86400.0`	Maximum allowed step size (s)
`safetyFactor`	`double`	`0.9`	PI controller safety factor
`minFactor`	`double`	`0.2`	Minimum step-size reduction factor
`maxFactor`	`double`	`5.0`	Maximum step-size growth factor

Fixed-Step Constructor¶

var fixedStep = new RK78Integrator(fixedStepSize: 30.0);

When created with a fixed step size, AdaptiveMode is false and the integrator uses constant steps.

Properties¶

Property	Description
`AbsoluteTolerance`	Configured absolute tolerance
`RelativeTolerance`	Configured relative tolerance
`AdaptiveMode`	`true` for adaptive PI control, `false` for fixed step

Key Features¶

Adaptive PI step control: Adjusts step size to maintain error within tolerances.
Sub-step event refinement: Uses BisectionEventFinder to locate event times to ~1e-10 s precision within a step via Hermite dense output.
Conformance-level accuracy: Validated against reference trajectories (LEO, GEO, SSO).

// Adaptive (default)
var integrator = new RK78Integrator(
    absoluteTolerance: 1e-10,
    relativeTolerance: 1e-10,
    initialStepSize: 30.0);

// Fixed-step
var fixedIntegrator = new RK78Integrator(fixedStepSize: 10.0);