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SympLie

SympLie is an experimental JAX package for simulating and differentiating controlled rigid-body attitude dynamics on \(SO(3)\). Its core is a Moser–Veselov variational integrator for rotational motion.

Capabilities

  • Torque-free and externally forced rigid-body integration on \(SO(3)\).
  • A composable single-step map for custom JAX scans and control loops.
  • The \(SO(3)\) maps and invariant diagnostics needed to use and inspect the integrator.
  • State-dependent torque under zero-order hold.
  • Fixed-target geometric PD attitude control.
  • Geometric attitude trajectory tracking.
  • Gyroscope attitude propagation with optional bias compensation.
  • Solver diagnostics, batched geometry, JIT compilation, and automatic differentiation.

Start with installation and examples, then read the frame and sampling conventions before using the dynamics APIs.

Scope

SympLie deliberately remains a rotational-dynamics package. It does not provide multibody dynamics, translation, contact, constraints, estimation, actuator allocation, or robotics middleware. It is not a replacement for jaxlie, Sophus, Drake, or Pinocchio. Its \(SE(3)\) exponential and logarithm utilities are not an \(SE(3)\) dynamics model.