Codes for the article The Zermelo Navigation Problem on the 2-Sphere of Revolution: An Optimal Control Perspective with Applications to Micromagnetism, from Bernard Bonnard, Olivier Cots and Yannick Privat.
The code in this repository is in Python and is based upon nutopy. It provides tools to compute objects from Riemannian geometry and its extensions.
The directory geometry2d contains generic functions to compute on the 2-sphere: geodesics, conjugate locus, wavefronts, spheres. It contains also the necessary functions to plot.
The directoy src contains the Hamiltonian associated to the Landau-Lifshitz equation (hfun.f90) and its derivatives. The files for the derivatives are computed thanks to the Tapenade software, see differentiate.sh. The Hamiltonian and its derivatives are written in Fortran and are wrapped in Python thanks to the file wrapper.py.
The notebook landau-finsler.ipynb compute the optimal synthesis of the article in the Finsler case and the notebook landau-billiard.ipynb is used to illustrate the Landau-Lifshitz billiard phenomenom.