GeometricProblems.jl

Collection of example problems with interesting geometric structure for GeometricIntegrators.jl.

Example Problems

• [x] ABC Flow,
• [x] Exponential Growth,
• [ ] Fermi-Pasta-Ulam Problem,
• [ ] Hénon-Heiles System,
• [ ] Kepler Problem,
• [x] Lorenz Attractor in 3D,
• [x] Lotka-Volterra in 2D,
• [x] Lotka-Volterra in 3D,
• [x] Lotka-Volterra in 4D,
• [x] Massless Charged Particle,
• [x] Harmonic Oscillator,
• [x] Coupled Harmonic Oscillator,
• [ ] Nonlinear Oscillators,
  • [ ] Duffing Oscillator,
  • [ ] Lennard-Jones Oscillator,
  • [ ] Mathews-Lakshmanan Oscillator,
  • [ ] Morse Oscillator,
• [x] Pendulum,
  • [x] Mathematical Pendulum,
  • [x] Double Pendulum,
• [x] Planar Point Vortices,
• [ ] Rigid Body,
• [ ] Chaplygin Sleigh,
• [ ] Inner Solar System,
• [ ] Outer Solar System,
• [ ] Heavy Top,
• [x] Toda lattice.

See ChargedParticleDynamics.jl for

• Charged Particle Motion in various electromagnetic Fields,
• Pauli Particle Dynamics in various electromagnetic Fields,
• Guiding Center Dynamics in various magnetic fields,
• Gyrokinetic Dynamics in various magnetic fields.

See GeometricExamples.jl for example scripts that run these problems with the integrators implemented in GeometricIntegrators.jl.

Development

We are using git hooks, e.g., to enforce that all tests pass before pushing. In order to activate these hooks, the following command must be executed once:

git config core.hooksPath .githooks