Solis 1 0 6 – Code's Editors Integrator

This page lists the available integrators within Tudat(Py) and provides code examples which illustrate their configuration.

1. Solis 1 0 6 – Codes Editors Integrator Software
2. Solis 1 0 6 – Codes Editors Integrator Edition

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classEuler¶

The Euler method is the simplest integrator that is available in Tudat. Awesome mails pro edition 4 80 – create interactive emails. It is known to be inaccurate for complex dynamics and is therefore discouraged for use in research. It can however still be used for comparison studies or very simple propagations.

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• initial_time

  Floating point value that defines the simulation's start epoch.

• fixed_step_size

  Floating point valuethat defines the fixed step-size to be used either by the euler or the rungeKutta4 numerical integrator.

• save_frequency

  Cadence at which to save the numerical integrated states. For instance, you may want to save one every 15 time steps, to give an output that is less demanding in terms of storage (in this case 15 would be the save_frequency). The default value is 1.

• assess_termination_on_minor_steps

  Determines whether the propagation termination conditions should be evaluated during each function evaluation (or ‘minor step') of the integrator (true) or only at the end of each integration step (false). The default value is false, and the termination conditions are only checked on each full step of the intergator.

Runge-Kutta4

The Runge-Kutta 4 integrator is a fixed step size integrator. It is a multistage method, meaning that it uses multiple stages (function evaluations) to perform a single time step. In the case of RK4, there are four stages.

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• initial_time

  Floating point value that defines the simulation's start epoch.

• fixed_step_size

  Floating point valuethat defines the fixed step-size to be used either by the euler or the rungeKutta4 numerical integrator.

• save_frequency

  Cadence at which to save the numerical integrated states. For instance, you may want to save one every 15 time steps, to give an output that is less demanding in terms of storage (in this case 15 would be the save_frequency). The default value is 1.

• assess_termination_on_minor_steps

  Determines whether the propagation termination conditions should be evaluated during each function evaluation (or ‘minor step') of the integrator (true) or only at the end of each integration step (false). The default value is false, and the termination conditions are only checked on each full step of the intergator.

Runge-Kutta-FehlbergandRunge-KuttaDormand-Prince

These variable-step multi-stage integrators allow for step size control using embedded Runge-Kitta methods, with the step size adaptation based on user-defined tolerances.

One of a number of different sets of coefficient sets for the embedded Runge-Kutta methods may be selected

• RKF4(5), defined by propagation_setup.integrator.RKCoefficientSets.rkf_45 (in Python)

• RKF5(6), defined by propagation_setup.integrator.RKCoefficientSets.rkf_56 (in Python)

• RKF7(8), defined by propagation_setup.integrator.RKCoefficientSets.rkf_78 (in Python)

• RKDP8(7), defined by propagation_setup.integrator.RKCoefficientSets.rkdp_87 (in Python)

These coefficient sets may be defined as follows:

The integrator settings for the variable step-size multi-stage integrator may be defined as follows:

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• initial_time

  Floating point value that defines the simulation's initial time.

• initial_time_step

  Floating point value that defines the initial step-size to be used by the numerical integrator.

• coefficient_set

  Setting that defines the coefficient set to be used by numerical integrator. The list of available coefficient sets is given above.

• minimum_step_size

  Floating point value that defines the minimum step-size that the numerical integrator can take.

• maximum_step_size

  Floating point value that defines the maximum step-size that the numerical integrator can take.

• relative_error_tolerance

  Floating point value that defines the relative error tolerance for step size control of the numerical integrator.

• absolute_error_tolerance

  Floating point value that defines the absolute error tolerance for step size control of the numerical integrator.

• save_frequency

  Cadence at which to save the numerical integrated states. For instance, you may want to save one every 15 time steps, to give an output that is less demanding in terms of storage (in this case 15 would be the save_frequency). The default value is 1.

• assess_termination_on_minor_steps

  Determines whether the propagation termination conditions should be evaluated during each function evaluation (or ‘minor step') of the integrator (True) or only at the end of each integration step (False). The default value is False, and the termination conditions are only checked on each full step of the intergator.

• safety_factor

  Safety factor for step size control. The default value is 0.8.

• maximum_factor_increase

  Maximum increase factor in time step in subsequent iterations. The default value is 4.0.

• minimum_factor_increase

  Minimum decrease factor in time step in subsequent iterations. The default value is 0.1.

Bulirsch-Stoer

The following different sequences are available for the Bulirsch-Stoer method in Tudat: Todoey 1 1 9 download free.

• Bulirsch-Stoer sequence;

• Deufelhard sequence.

These are available in the propagation_setup.ExtrapolationMethodStepSequences enum and must be supplied to the Python function that initializes the integrator, as shown below:

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In addition, the save_frequency, assess_termination_on_minor_steps, safety_factor, maximum_factor_increase and minimum_factor_increase inputs may optionally be provided, as fpr the simulation_integrator_type_rkf_and_rkdp, with the difference that the defaults for the last two optional inputs are 10.0 and 0.1, respectively.

Adams-Bashforth-Moulton

The last integrator in the list is a multi-step, predictor-corrector method. It uses multiple time steps in its approximation of the next step and is implicit, meaning that it needs a predictor-corrector setup to solve for the unknown time step. Its order is the number of steps used to predict the next value, so an order of two means that steps n-1 and n are used to predict n+1.

Bounds on the used order must be given to the Python function initializing the integrator, next to the customary arguments:

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In addition, the save_frequency and assess_termination_on_minor_steps inputs may optionally be provided, as fpr the simulation_integrator_type_rkf_and_rkdp.

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Solis 1 0 6 – Codes Editors Integrator Software

These are available in the propagation_setup.ExtrapolationMethodStepSequences enum and must be supplied to the Python function that initializes the integrator, as shown below:

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In addition, the save_frequency, assess_termination_on_minor_steps, safety_factor, maximum_factor_increase and minimum_factor_increase inputs may optionally be provided, as fpr the simulation_integrator_type_rkf_and_rkdp, with the difference that the defaults for the last two optional inputs are 10.0 and 0.1, respectively.

Adams-Bashforth-Moulton

The last integrator in the list is a multi-step, predictor-corrector method. It uses multiple time steps in its approximation of the next step and is implicit, meaning that it needs a predictor-corrector setup to solve for the unknown time step. Its order is the number of steps used to predict the next value, so an order of two means that steps n-1 and n are used to predict n+1.

Bounds on the used order must be given to the Python function initializing the integrator, next to the customary arguments:

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In addition, the save_frequency and assess_termination_on_minor_steps inputs may optionally be provided, as fpr the simulation_integrator_type_rkf_and_rkdp.

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Key Code Media and Canon U.S.A., Inc., a leader in digital imaging solutions, are partnering up to deliver their customers a better system integrator experience. As an authorized Canon U.S.A., Inc., system integrator, through this program, Key Code Media will be able to provide its customers with high-quality Canon products, including the company's Cinema EOS Cameras and Lenses, Broadcast Lenses, DSLRs and mirrorless cameras, and EF and RF Lenses.

'As an Authorized Canon System Integrator, Key Code Media can provide our customers with a greater breadth of camera technologies through Canon's digital imaging products to support our clients' production requirements.'

In addition to direct access to Canon's equipment, the Canon System Integrator program is designed to provide Canon U.S.A., Inc.'s authorized channel partners with the resources necessary to help effectively utilize the company's incredible arsenal of products and technologies.

'We are excited to work closer with one of the top integrators in the United States, Key Code Media, through our new System Integrator program. Key Code Media has a deep understanding of camera needs for house of worship, education, and corporate markets. Canon cameras and lenses have been adopted by the media and entertainment industries for years, and we're excited to introduce them further to new areas with Key Code Media.'

Key Code Media's ten nationwide office locations will be offering Canon products across the United States. As always, when customers purchase equipment through Key Code Media, it is backed by our highly experienced and engaged customer sales team, and can be configured and installed by our bench of support engineers.

Solis 1 0 6 – Codes Editors Integrator Software

Solis 1 0 6 – Codes Editors Integrator Edition

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