Talk:Solving the geodesic equations/to do

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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