GeometricProblems.jl

GeometricProblems.jl is a collection of ODEs and DAEs with interesting geometric structures together with useful diagnostics and plotting tools.

Typical structures are

• Variational structure, i.e., the equations can defined in terms of a Lagrangian function and be obtained from an action principle;
• Hamiltonian structure, i.e., the equations can be defined in terms of a Hamiltonian function together with a symplectic or Poisson matrix;
• Invariants, i.e., the equations have symmetries and associated conservation laws;
• Volume preservation, i.e., the flow of the equations is divergence-free.

Contents

• Diagnostics
• Hénon-Heiles System
• Kepler Problem
• Lorenz Attractor in 3d
• Lotka-Volterra 2d
• Lotka-Volterra 3d
• Lotka-Volterra 4d
• Massless Charged Particle
• Harmonic Oscillator
• Nonlinear Oscillators
• Mathematical Pendulum
• Double Pendulum
• Planar Point Vortices
• Inner Solar System
• Outer Solar System

References

If you use the figures or implementations provided here, please consider citing GeometricIntegrators.jl as

@misc{Kraus:2020:GeometricIntegratorsRepo,
  title={GeometricIntegrators.jl: Geometric Numerical Integration in Julia},
  author={Kraus, Michael},
  year={2020},
  howpublished={\url{https://github.com/JuliaGNI/GeometricIntegrators.jl}},
  doi={10.5281/zenodo.3648325}
}

as well as this repository as

@misc{Kraus:2020:GeometricProblemsRepo,
  title={GeometricProblems.jl: Collection of Differential Equations with Geometric Structure.},
  author={Kraus, Michael},
  year={2020},
  howpublished={\url{https://github.com/JuliaGNI/GeometricProblems.jl}},
  doi={10.5281/zenodo.4285904}
}

Figure License

Copyright (c) Michael Kraus <michael.kraus@ipp.mpg.de>

All figures are licensed under the Creative Commons CC BY-NC-SA 4.0 License.

Software License

Copyright (c) Michael Kraus <michael.kraus@ipp.mpg.de>

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.