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Gurplesnork (talk | contribs) m In the Examples section, the link for reparametrization invariance was changed to point at the Invariance section of Paramateriztion (Geometry), previously it was redirecting to the page for parametric curves where there was no discussion of reparameterization invariance. |
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==Examples==
Consider the dynamics of a single point particle of mass {{mvar| m}} with no internal degrees of freedom moving in a [[pseudo-Riemannian]] spacetime manifold {{mvar|S}} with [[metric tensor|metric]] '''g'''. Assume also that the parameter {{mvar|τ}} describing the trajectory of the particle is arbitrary (i.e. we insist upon [[
If we coordinatize ''T'' * ''S'' by its position {{mvar|x}} in the base manifold {{mvar|S}} and its position within the cotangent space '''p''', then we have a constraint
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