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For the torus  :
Differential system of equations:  .
Writing  , differential equation:  , where c is a constant. |
The resolution of the above differential equation leads to elliptic integrals.
The geodesics can be wound or not; even when they are, they are not toric solenoids (except in the limit cases of meridians and the 2 principal circles).
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| Geodesic of the horn torus | Geodesic of the spindle torus |
See also the asymptotic lines of the torus.
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© Robert FERRÉOL 2018