HCRP project 2009
geodesics on torus of revolution
Geodesics on torus of revolution
Office: SciCtr 434

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)};

Higher order caustics

Second order caustic Forth order caustics
Questions and comments to knill@math.harvard.edu
Oliver Knill | Department of Mathematics | Harvard University