geomech

Symbolic derivation of equations of motion on smooth manifolds.

geomech uses variational calculus on Lie groups to derive globally valid, singularity-free equations of motion.

What it does

Given a Lagrangian and virtual work, geomech automatically derives globally valid, singularity-free equations of motion on Lie groups (\(SO(3)\), \(S^2\)) using Hamilton's principle and variational calculus -- no Euler angles or quaternions required.

The pipeline:

1. Define symbolic scalars, vectors, and matrices
2. Build kinetic/potential energy and virtual work expressions
3. Call compute_eom() -- the library takes variations, applies the product rule, expands, integrates by parts, simplifies, and extracts the equations

Quick links

• Getting Started -- installation and first example
• Examples -- point mass, spherical pendulum, rigid body
• API Reference -- auto-generated from source

Citation

If you use geomech in your research, please cite this package along with corresponding original work, Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds and Symbolic Computation of Dynamics on Smooth Manifolds.

@software{kotaru2026geomech,
  title={geomech: Symbolic toolbox for geometric mechanics on smooth manifolds},
  author={Kotaru, Prasanth},
  url={https://github.com/vkotaru/pygeomech},
  year={2026}
}