The Lagrangian Mechanics Simulator (LMS) is a Python library designed for the simulation of mechanical systems using Lagrangian mechanics. Lagrangian mechanics provides a powerful framework for describing the dynamics of complex systems by expressing them in terms of generalized coordinates, velocities, and potential energy functions.
The library introduces a parametrization function that allows users to wrap constraint functions, facilitating the definition of constraints within a Lagrangian system. This modularity enables the easy incorporation of various constraints into mechanical simulations.
The library provides a potential_energy function that allows users to wrap potential energy functions, offering flexibility in defining energy contributions within a Lagrangian system. Users can easily incorporate gravitational and elastic potential energy functions into their simulations.
The evolve_lagrangian function serves as a core component for dynamically evolving Lagrangian systems over specified time spans. This function integrates the equations of motion using the Euler-Lagrange equations, providing users with a predictive tool for simulating the behavior of mechanical systems.
import jax
from jax import numpy as jnp
from src.surfaces import parametrization, double_pendulum
from src.potentials import potential_energy, gravity
from src.lagrangian import evolve_lagrangian
from src.plotting import animate_3D_trajectory
# Set initial conditions and parameters
nbodies = ndim = 2
mass = jax.random.uniform(key, (nbodies,))
q = jax.random.uniform(key, (nbodies, ndim))
q_t = jax.random.uniform(key, (nbodies, ndim))
# Create a constraint with parametrization
constraint = parametrization(double_pendulum, l1=1.0, l2=2.0)
# Create gravitational potential energy
g_pot = potential_energy(gravity, g=9.81)
# Set time evolution parameters
tmax = 20.
npoints = 500
tspan = jnp.linspace(0., tmax, npoints)
# Evolve the Lagrangian system
positions, velocities = evolve_lagrangian(tspan, q, q_t, mass, potentials=[g_pot], constraint=constraint)
# animate the trajectory
animate_3D_trajectory(tspan, positions, constraint)
To use the Lagrangian Mechanics Simulator, you can clone the repository and install the required dependencies:
git clone https://github.com/lorenzoliuzzo/LMS.git
cd LMS
pip install -r requirements.txtIf you want to contribute to the project, you can open a pull requests or use the issue tracker to suggest any code implementations or report bugs. Any contributions are welcome!
The code is released under the terms of the GNU General Public License v3.0, see the LICENSE.