RK89 Object

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Description

The Runge Kutta 8(9) propagator uses 8th order Runge-Kutta propagation with 9th order error control to propagate the spacecraft orbit. See expanded description.

 

Runge Kutta 8(9) solves the Cartesian formulation of the orbit equations of motion using a Runge-Kutta 8(9) integrator. This method consumes more memory than the other Runge Kutta integrators but takes fewer propagation steps for a specified accuracy. The RK8(9) Propagator is a ninth order embedded Runge-Kutta integrator that maintains eighth order numerical accuracy. This integrator uses Fehlberg-style embedding, with coefficients derived by Verner. Integration with the RK8(9) integrator proceeds through sixteen intermediate stages, accumulating data from each stage and using these data to produce a final, accurate integration step. The RK8(9) Propagator uses the ICRF representation of the orbital elements, expressed in the Cartesian coordinate system (ICRF Cartesian coordinates) to represent the spacecraft’s state for integration. To this state it applies the forces specified in the ForceModel (also expressed in ICRF Cartesian coordinates) in order to determine how to move the spacecraft through time. The RK8(9) Propagator can be run in either fixed-step or variable-step mode. When the propagator is run in variable step mode, the integration step size is controlled by the user-specified error tolerance. Each integration step can have a different step size. This mode allows FreeFlyer to move the spacecraft in time (i.e., propagates the spacecraft) with the largest possible time step consistent with the specified error tolerance. The fixed-step mode ensures that every propagation step moves the spacecraft the same amount of time. FreeFlyer maintains the specified error tolerance for fixed step propagation by keeping the step size at the specified step size when the tolerance would allow a larger time step. If the tolerance forces the time step to be smaller than the specified value, FreeFlyer will take multiple steps internally, and report the results after the accumulated propagation reaches the desired time step.

 

 

Inheritance Hierarchy: Object->Propagator->Integrator->RK89

 

Available In Editions:

Engineer

Mission

 

Timing Precision Mode

This page describes functionality in nanosecond timing precision mode.

Click here to see the documentation for this object in millisecond timing precision mode.

 

Constructors

 

Signatures

Description

RK89()

Create a default RK89 object.

RK89(ForceModel forceModel)

Create a RK89 using the specified ForceModel.

 

 

 

Properties

 

Name

Description

Attributes

AllowErrorViolation

Determines whether the error tolerance may be violated once the minimum step size is reached. If this property is set to true, and the integrator step error does not meet the tolerance at 1 ms step size, the state is automatically advanced 1 ms ahead and a warning is generated.

Type:   Variable

Access: Read/Write

CalculateSTM

Flag indicating whether or not to calculate the state transition matrix at each integration step as part of the state integration. If the PropagateCovariance flag is set to true on the SpacecraftODProperties object or if the Spacecraft is in an estimation process, the STM is always calculated. If the Spacecraft.Propagator is not an Integrator type then this property is ignored.

Type:   Variable

Access: Read/Write

DeclaredName

The name of the object as declared.

Type:   String

Access: Read-Only

DisplayName

The name displayed for this object in output windows such as views, plots, and reports.

Type:   String

Access: Read/Write

FixedStep

Flag denoting whether the propagator is being run in fixed-step mode (i.e. constant StepSize) or in variable-step mode (i.e. variable StepSize).

Type:   Variable

Access: Read/Write

ForceModel

A force model.

Type:   ForceModel

Access: Read-Only

LargeCurvature

Flag that signifies whether the integration has failed due to a large curvature in the force field. (1 = Integration Failed, 0 = Integration Nominal, -1 = No Integration has been performed).

Type:   Variable

Access: Read-Only

MaxTries

The maximum number of times to attempt to change the step size in the integration process in order to meet the specified error tolerance. If the specified error tolerance is not met after MaxTries attempts, an error is thrown.

Type:   Variable

Access: Read/Write

ObjectId

The unique identifier for the object.

Type:   Variable

Access: Read-Only

ObjectType

The type of the object.

Type:   String

Access: Read-Only

RelativeErrorThreshold

If the absolute error is less than this value, then the absolute error is compared against the tolerance. Otherwise the relative error is compared against the tolerance.

 

Set a very large value (e.g. 1e100) to ensure the RK89.Tolerance is treated as an absolute error tolerance. Set a very small value (e.g. 1e-100) to ensure that the RK89.Tolerance is treated as a relative error tolerance.

Type:   Variable

Access: Read/Write

StepJustTaken

The size of the previous step taken by the integration process.

Type:   TimeSpan

Access: Read-Only

Units:   s

StepsAttempted

This represents the sum of the successful and failed steps. This property will closely reflect the performance of the integrator since it is a measure of the total number of steps executed by the integrator.

Type:   Variable

Access: Read-Only

StepsFailed

This property is incremented once each time the integrator steps the spacecraft forward and the integrator tolerance is not met. A high ratio of the number of failed to successful steps may suggest that the integrator tolerance is too high.

Type:   Variable

Access: Read-Only

StepSize

The number of seconds the propagated object is advanced when the Step command is executed.

Type:   TimeSpan

Access: Read/Write

Units:   s

StepsRequested

Represents the count of integration steps requested by the user. This property will be incremented once each time the FreeFlyer engine advances the spacecraft to a desired epoch. For the Step command, this property will be incremented once. For interval methods and Step-to commands, this property will be incremented each time bisection is performed unitl the condition is met. Abnormally high values on this property can indicate that the IntervalStopAccuracy may be too strict.

Type:   Variable

Access: Read-Only

StepsSuccessful

This property is incremented for every successful step of the integrator. Since it may take several steps to reach the desired epoch at the specified tolerance, the number of successful steps may be greater than the number of requested steps.

Type:   Variable

Access: Read-Only

StepToTake

The maximum possible size of the next step to take in the integration process based on the relative error tolerance. When the StepSize property is set, this property is initialized with the new StepSize value and is updated after the next step is taken.

Type:   TimeSpan

Access: Read-Only

Units:   s

STM

Returns the State Transition Matrix. The matrix is always a square where the length of each side is determined by the total number of properties being estimated or considered.

Type:   Matrix

Access: Read-Only

STMCalculationMethod

A flag indicating the method to be used to calculate the state transition matrix. Note that even if the CalculateSTM property is set to false, this property still applies if the SpacecraftODProperties.PropagateCovariance flag is to true or if the Spacecraft is included in an estimation process.

Type:   Variable

Access: Read/Write

Tolerance

When the Step command is executed, intermediate integration steps are taken to ensure that the local error never exceeds this value.

Type:   Variable

Access: Read/Write

ToleranceMode

Determines how the relative error tolerance is calculated.

Type:   Variable

Access: Read/Write

 
 

 

Methods

 

Name

Description

ClearSavedStates

Clears previous saved states for this object.

GetFromFile

Load the object state from the specified FreeFlyer object file.

GetFromString

Load the object state from the specified string.

PutToFile

Convert the object state to FreeFlyer object xml and write to a file.

PutToString

Convert the object state to FreeFlyer object xml and return as a string.

ReferenceEquals

Returns 1 if the argument refers to the calling object and 0 otherwise.

ResetStepStatistics

Resets the Integrator step counters back to zero. The step counters will continue incrementing the next time the spacecraft is stepped.

Restore

Restore an object's state from a previously saved state.

Save

Save the object's state so that it can be restored later.

 
 

 

 

See also

Spacecraft Propagators

Setting up an Integrator