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