Euler-Lagrange

This package generates code for the Euler-Lagrange equations as well as Hamilton's equations for GeometricIntegrators.jl and related packages.

Installation

EulerLagrange.jl and all of its dependencies can be installed via the Julia REPL by typing

]add EulerLagrange

Usage

Using EulerLagrange.jl is very simple and typically consists of four to five steps:

1. Obtain symbolic variables for a Lagrangian or Hamiltonian system of a given dimension.
2. Obtain a symbolic representation of the parameters of the system if it has any.
3. Build the Lagrangian or Hamiltonian using those symbolic variables and parameters.
4. Construct a LagrangianSystem or HamiltonianSystem, which is where the actual code generation happens.
5. Generate a LODEProblem or HODEProblem that can then be solved with GeometricIntegrators.jl.

Details for the specific system types can be found on the following pages:

• Hamiltonian Systems
• • Harmonic Oscillator
• Lagrangian Systems
• • Particle in a potential
  • Parameters
• Degenerate Lagrangian Systems
• • Lotka-Volterra
• Caveats
• • Simplicity
  • Parameters
  • Initial Guesses

References

If you use EulerLagrange.jl in your work, please consider citing it by

@misc{Kraus:2023:EulerLagrange,
  title={EulerLagrange.jl: Code generation for Euler-Lagrange equations in Julia},
  author={Kraus, Michael},
  year={2023},
  howpublished={\url{https://github.com/JuliaGNI/EulerLagrange.jl}},
  doi={10.5281/zenodo.8241048}
}