Feature/1004 stochastic dynamics

[juan-g-bonilla]

• Tickets addressed: Closes Support Stochastic Integration #1004
• Review: By commit
• Merge strategy: Merge (no squash)

Description

This PR introduces support for stochastic differential equations (SDEs) in the Basilisk simulation framework. The main changes include:

• State Diffusion Support: The state machinery (StateData, DynParamManager, ExtendedStateVector, etc.) is extended to support setting and propagating the diffusion term (g_i) for multiple noise sources, in addition to the deterministic drift (f).
• Stochastic Integrators: Implements weak second-order stochastic Runge-Kutta (SRK) integrators, specifically the methods described by Tang & Xiao (2017), including both W2-Ito1 and W2-Ito2 schemes. These are available as svStochIntegratorW2Ito1 and svStochIntegratorW2Ito2. Also implements the Euler-Mayurama integrator (available in svStochIntegratorMayurama.
• Noise Source Management: Adds machinery to register and share noise sources between states, allowing for correlated stochastic processes across different states.
• DynamicObject Interface: Adds equationsOfMotionDiffusion to DynamicObject and relevant subclasses, enabling models to compute the diffusion term.
• MuJoCo Integration: Updates the MuJoCo scene and state classes to support stochastic integration, including proper propagation of diffusions.
• spacecraft Integration: equationsOfMotionDiffusion calls the regular equationsOfMotion so that stateEffectors can set the diffusion of states.
• Python Bindings: Updates SWIG interfaces and Python helper functions to expose the new stochastic integrators and noise management features.
• Unit Test: Adds a new test (test_stochasticIntegrators.py) that demonstrates and validates the new stochastic integration capabilities.
• Scenario: Adds a new scenario scenarioStochasticDrag.

Commits are organized by subsystem: core state machinery, integrator implementation, MuJoCo support, Python bindings, and tests.

Verification

• Automated Tests: Added a new unit test (test_stochasticIntegrators.py) that exercises the stochastic integrator on a simple exponential system and an example from the reference paper. The test compares Basilisk's results to a pure Python implementation.
• Backwards Compatibility: Existing deterministic integrators and state propagation remain unaffected.

Documentation

• Code Documentation: All new classes and methods are documented inline with Doxygen-style comments. Python methods have docstrings.
• Scenario: scenarioStochasticDrag illustrates how to use a stochastic state.

Future work

• Additional Integrators: Implement strong-order stochastic integrators, support for adaptive time-stepping, Stratonovich noise integrators...