Give me (L(q,\dot q,t)) and I’ll give you the motion. This repo auto-derives the Euler–Lagrange equations with SymPy and integrates the resulting ODEs with SciPy. It includes ready-to-run examples (pendulum, double pendulum, N-body gravity, and spring–mass networks) and lightweight animations.

• Symbolically derive Euler–Lagrange equations from a user-specified Lagrangian (SymPy).
• Convert to first-order ODEs and integrate (SciPy solve_ivp).
• Jupyter notebooks with visualizations and energy-drift diagnostics.

• python3 -m venv .venv
• source .venv/bin/activate
• pip install -r requirements.txt
• pip install -e .

• notebooks/01_simple_pendulum_lib.ipynb — minimal library usage.
• notebooks/02_double_pendulum.ipynb — chaotic two-link example.
• notebooks/03_springs_random.ipynb — 4-mass spring ring with random initialization and animation.

pre-commit run --all-files

pytest -q

pytest --cov=src/euler_lagrange_solutions --cov-report=term-missing

MIT Licence

If you use this code in academic work, please cite the repository.

• End-to-end EL pipeline (symbolic → numeric → integration).
• Clean, modern Python: type hints, tests, CI, pre-commit.
• Clear demos with small, readable notebooks + animations.