Geodetic Coils on Deformed Sphere

Details Geodetic Coils on Deformed Sphere Geodetic Coils on Deformed Sphere

2005-07-11

arxiv.org/abs/math/0507206v1

Mathematics

Dynamical Systems

12 pages, 14 figures

Scientific paper

We study geodetic lines on a surface generated by a small deformation of the standard 2D-sphere. We construct an auxiliary hamiltonian system with the view of describing geodetic coils and almost closed geodesics, by using the fact that loops of the coil can be well approximated by great circles of the sphere. The phase space of the auxiliary system is determined by the graph generated by separatrixes of its solutions, the vertices of the graph corresponding to almost closed geodesics and the edges to the geodetic coils joining them. Topological types of the graph depend on the parameters determining the deformation. Using the method of averaging in conjunction with the computer modelling of the auxiliary system, we obtain a fairly detailed visualization of geodesics on the deformed sphere.

Affiliated with

Also associated with

No associations

Rating

Geodetic Coils on Deformed Sphere does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Geodetic Coils on Deformed Sphere, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geodetic Coils on Deformed Sphere will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-404682