Jacobi least time vs. Fermat Hamilton

[andrewr]

Could anyone give me a simple explanation as to why the Fermat/Hamilton principle would be called more general than the Jacobi least time principle? I am trying to understand what differences would result from using the one principle vs. the other; eg: where/in what way would the Jacobi least time be inferior?

I know basic ODE, PDE, linear algebra, and variational methods. I have a BSEE background.

Thanks.

 

[RedX]

I googled "Jacobi least time" and didn't get any results. I know what the Fermat/Hamiltonian principle is though. Could you describe the Jacobi least time principle? Maybe people might know it by a more common name.

 

[RedX]

Oh I see. Here's some lecture notes that explains it from baez's website:

http://math.ucr.edu/home/baez/classical/cm05week05.pdf

 

[andrewr]

Oh I see. Here's some lecture notes that explains it from baez's website:

http://math.ucr.edu/home/baez/classical/cm05week05.pdf

Thank you, that helps. The literature I was reading was ambiguous, I think "Jacobi least time" is supposed to be "Fermat's least time" and the author switched the names, or meant Jacobi's analogy of Fermat's principle for particles.

I still don't understand why one principle (either) would be more general than the other. Is "least time" ever inferior to "least action"? or vice versa?

--Thanks.