MechanicsDSL provides a powerful computational physics framework designed for physicists, researchers, and educators to effortlessly define and simulate complex physical systems. Leveraging a user-friendly, LaTeX-inspired syntax, this framework automates the generation of high-performance simulations, ranging from pendulums to planetary orbits, as well as complex fluid dynamics.

Key Features

• Symbolic Engine: Derives equations of motion automatically from Lagrangians or Hamiltonians.
• Multiple Code Generators: Supports generation of C++, Rust, Julia, CUDA, WebAssembly, Unity, Unreal, Modelica, and more.
• GPU Acceleration: Utilizes a JAX backend for JIT compilation and automatic differentiation, enhancing performance.
• Inverse Problems: Facilitates parameter estimation, sensitivity analysis, and MCMC uncertainty quantification.
• Jupyter Notebook Integration: Employs %%mechanicsdsl magic commands for seamless use in Jupyter notebooks.
• Real-time API: Implements a FastAPI server with WebSocket streaming for real-time simulation interactions.
• IDE Support: Offers an LSP server for Visual Studio Code, complete with autocomplete and diagnostics capabilities.
• Plugin Architecture: Features an extensible system that allows for custom physics domains and solvers.

Core Capabilities

MechanicsDSL encompasses a range of areas in physics, including:

• Classical Mechanics: Features modules for Lagrangian and Hamiltonian mechanics, stability analysis, and perturbation theory.
• Quantum Mechanics: Addresses bound states, scattering, quantum tunneling, and semiclassical phenomena.
• Electromagnetism: Covers charged particles, wave behavior, antennas, and waveguides.
• General Relativity: Helps simulate black holes, geodesics, lensing effects, and cosmological models.
• Thermodynamics: Includes heat engine simulations, equations of state, and phase transitions.
• Fluid Dynamics: Integrates an SPH solver for simulating incompressible fluids.

Quick Start

Example of the Figure-8 Three-Body Orbit

Here’s how to define and simulate a gravitational three-body system in MechanicsDSL:

from mechanics_dsl import PhysicsCompiler

# Define the system using LaTeX-inspired DSL
figure8_code = r"""
\system{figure8_orbit}
\defvar{x1}{Position}{m} \defvar{y1}{Position}{m}
\defvar{x2}{Position}{m} \defvar{y2}{Position}{m}
\defvar{x3}{Position}{m} \defvar{y3}{Position}{m}
\defvar{m}{Mass}{kg} \defvar{G}{Grav}{1}

\parameter{m}{1.0}{kg} \parameter{G}{1.0}{1}

\lagrangian{
    0.5 * m * (\dot{x1}^2 + \dot{y1}^2 + \dot{x2}^2 + \dot{y2}^2 + \dot{x3}^2 + \dot{y3}^2)
    + G*m^2/\sqrt{(x1-x2)^2 + (y1-y2)^2}
    + G*m^2/\sqrt{(x2-x3)^2 + (y2-y3)^2}
    + G*m^2/\sqrt{(x1-x3)^2 + (y1-y3)^2}
}
"""

# Compile and simulate
compiler = PhysicsCompiler()
compiler.compile_dsl(figure8_code)
compiler.simulator.set_initial_conditions({
    'x1': 0.97000436, 'y1': -0.24308753, 'x1_dot': 0.466203685, 'y1_dot': 0.43236573,
    'x2': -0.97000436, 'y2': 0.24308753, 'x2_dot': 0.466203685, 'y2_dot': 0.43236573,
    'x3': 0.0,        'y3': 0.0,        'x3_dot': -0.93240737, 'y3_dot': -0.86473146
})
solution = compiler.simulate(t_span=(0, 6.326), num_points=2000)

Fluid Dynamics Simulation

Simulating fluid dynamics is straightforward with the integrated SPH solver:

from mechanics_dsl import PhysicsCompiler

fluid_code = r"""
\system{dam_break}
\parameter{h}{0.04}{m}
\parameter{g}{9.81}{m/s^2}

\fluid{water}
\region{rectangle}{x=0.0 .. 0.4, y=0.0 .. 0.8}
\particle_mass{0.02}
\equation_of_state{tait}

\boundary{walls}
\region{line}{x=-0.05, y=0.0 .. 1.5}
\region{line}{x=1.5, y=0.0 .. 1.5}
\region{line}{x=-0.05 .. 1.5, y=-0.05}
"""

compiler = PhysicsCompiler()
compiler.compile_dsl(fluid_code)
compiler.compile_to_cpp("dam_break.cpp", target="standard", compile_binary=True)

For additional tutorials and examples, see the documentation. MechanicsDSL enables comprehensive exploration and simulation of physical systems, making it an invaluable tool for anyone engaged in computational physics.