HCRP project 2009

geodesics on torus of revolution

Geodesics on torus of revolution

Office: SciCtr 434

Email: knill@math.harvard.edu

Geodesics on a torus of revolution. This dynamical system is integrable as in any surface of revolution. | |

The primary caustic can already be complicated for a rotationally symmetric torus of revolution. There are directions, in which the geodesic winds around the torus several times before the Jacobi field reaches a zero. For these pictures, 120'000 geodesics have been started from one point and integrated until time 2PI. Always the first point was marked, where the Jacobi field is zero. |

Similar picture as above but with | r(u,v)={(2+(1+cos(u)/5) cos(v)) cos(u),(2+(1+cos(u)/5) cos(v))sin(u),sin(v)}; |

Second order caustic | Forth order caustics |

Questions and comments to knill@math.harvard.edu