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Recently, over in the relativity forum, Micromass contributed a post:
https://www.physicsforums.com/showpost.php?p=4168973&postcount=89
giving a proof that the most general coordinate transformation preserving the property of zero acceleration (i.e., maps straight lines to straight lines) is of fractional-linear form.
I'm now wondering whether there are generalizations of this sort of thing applicable to, e.g., trajectories of constant acceleration (i.e., nonzero, but constant acceleration), and maybe also trajectories of constant jerk?
[ http://en.wikipedia.org/wiki/Jerk_(physics) ]
1. What is the most general coordinate transformation (in 1+1D for starters) that maps curves of constant acceleration into curves of constant acceleration?
2. Is there already a well-developed body of math covering such cases, perhaps generalizing the theory of projective spaces that arise from an ambient linear space?
(P.S: I wasn't sure whether to ask this under Calculus, or Group Theory, or General Math. It kinda reaches into several categories.)
(P.P.S: Haven't tried using bold font in questions before. Thought I'd try it here since it seems to work for Tom Stoer... :-)
https://www.physicsforums.com/showpost.php?p=4168973&postcount=89
giving a proof that the most general coordinate transformation preserving the property of zero acceleration (i.e., maps straight lines to straight lines) is of fractional-linear form.
I'm now wondering whether there are generalizations of this sort of thing applicable to, e.g., trajectories of constant acceleration (i.e., nonzero, but constant acceleration), and maybe also trajectories of constant jerk?
[ http://en.wikipedia.org/wiki/Jerk_(physics) ]
1. What is the most general coordinate transformation (in 1+1D for starters) that maps curves of constant acceleration into curves of constant acceleration?
2. Is there already a well-developed body of math covering such cases, perhaps generalizing the theory of projective spaces that arise from an ambient linear space?
(P.S: I wasn't sure whether to ask this under Calculus, or Group Theory, or General Math. It kinda reaches into several categories.)
(P.P.S: Haven't tried using bold font in questions before. Thought I'd try it here since it seems to work for Tom Stoer... :-)
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