Talk:Solving the geodesic equations

From Wikipedia, the free encyclopedia

	Portal This article is within the scope of WikiProject Physics, which collaborates on articles related to physics.
Stub	This article has been rated as Stub-Class on the assessment scale.
Low	This article is on a subject of low importance within physics.
Help with this template This article has been rated but has no comments. If appropriate, please review the article and leave comments here to identify the strengths and weaknesses of the article and what work it will need.

This article has been automatically assessed as Stub-Class by WikiProject Physics because it uses a stub template.

If you agree with the assessment, please remove {{Physics}}'s auto=yes parameter from this talk page.
If you disagree with the assessment, please change it by editing the class parameter of the {{Physics}} template, removing {{Physics}}'s auto=yes parameter from this talk page, and removing the stub template from the article.

To-do list for Solving the geodesic equations:	edit · history · watch · refresh
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

To-do list for Solving the geodesic equations:

edit · history · watch · refresh

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

[edit] Confused edits ?

The iteration process for allegedly solving the geodesic equations (GE) given in the article does not actually describe how to solve for the geodesic equation. Rather, it seems to give some sort of consistency check for solutions of the Einstein field equations (EFE). Also, the exact solutions section makes the same mistake of confusing the EFE with the GE and tends to focus on vacuum solutions for some reason. Hmmm... MP (talk) 10:21, 12 February 2006 (UTC)

yep. sorry. what you did is much better.Complexica 22:34, 15 February 2006 (UTC)

[edit] Language links in GR articles

The language links in any article should be for that same defining article in another language, no ? MP (talk) 18:14, 16 February 2006 (UTC)

[edit] Minor cleanup

Hi CH EMS. I've tried to improve the article ever so slightly. Not feeling so great today (flu). I'm trying to do what I promised, namely, to try and improve the GR articles so we can get Wikiproject GTR off the ground. MP (talk) 15:33, 21 March 2006 (UTC)

Hi, MP! I'm busy with something else (arghgghgh) but the next thing on my todo list is to write in another venue an introduction to symmetries of ODEs and systems of ODEs, then use that as a basis for exactly the topic at hand, how to analyze/solve the geodesic equations for Riemannian and semi-Riemannian manifolds, with lots of examples. I have dozens of pages of notes for this plus dozens of maple worksheets illustrating some really nifty examples. My hope is to start with the simplest stuff and gradually up the ante, as JB puts it. Anyway, it would be great if you could you use that as a basis for Revision, Mark III, provided I can finish it. (Naturally I plan to put this up in ps/pdf, but I'd give you the latex file too.) But if I hope to start in a week and to finish both in a week, realistically, this probably means I'll get to it in a month or two and finish them sometime this Fall :-/ Hope you are feeling better soon! ---CH 16:05, 21 March 2006 (UTC)

I was able to fill out a few sections, but most of this is beyond my expertise. It's worth noting that I replaced differentiation by t by differentiation by s, since t has a special meaning in physics, and the geodesic equations aren't valid if time is used. Anarchic Fox 20:10, 22 July 2007 (UTC)