GeometricProblems.jl

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

Example Problems

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

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.