Talk:Solving the geodesic equations/to do
Tasks for expert:
- write and link to articles on point symmetry groups for ODEs and systems of ODEs
- write and link to article on the many faces of Noether's theorem
- rewrite this article along the following lines:
- geodesic Lagrangian to obtain the geodesic equations (and later to define Noether symmetries)
- heuristics on good coordinate charts
- effective potentials
- can try to eliminate one variable to reduce system to a single higher order equation in just one coordinate (c.f. example of spherical geodesics in appropriate chart)
- point symmetry group and relation with first integrals
- point symmetries related to the "affine" in affine parameter
- connection of Noether and variational symmetries with Killing vectors and Killing tensors
- examples should include at least S2 in (polar chart), H2 (UHS chart), S3 (Hopf torus chart), and some simple exact solutions in general relativity such as a pp-wave spacetime
- references should include Stephani, Differential Equations: their Solutions using Symmetries
Tasks for anyone:
- improve spelling and diction as needed
Talk pages are where people discuss how to make content on Wikipedia the best that it can be. You can use this page to start a discussion with others about how to improve the "Solving the geodesic equations/to do" page.
