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3 votes
0 answers
46 views

Relating Brachistochrone problem to Fermat's principle of least time [closed]

When I came across the Brachistochrone problem, my teacher said we could relate it to Fermat's principle of least time. So, we could make many glass slabs of high $\mathrm dx$, and every slab has a ...
AANT's user avatar
  • 31
5 votes
3 answers
630 views

Is Principle of Least Action a first principle? [closed]

It is on the basis of Principle of Least Action, that Lagrangian mechanics is built upon, and is responsible for light travelling in a straight line. Is its the classical equivalent of Schrodinger's ...
megamonster68's user avatar
1 vote
1 answer
175 views

Fermat's principle in classical mechanics?

I do know the principle of least action, but is it possible to formulate classical mechanics based on the principle of least time? That is, if we know the initial state $(x_i,p_i)$ of the particle and ...
Hulkster's user avatar
  • 735
18 votes
7 answers
2k views

When/why does the principle of least action plus boundary conditions not uniquely specify a path?

A few months ago I was telling high school students about Fermat's principle. You can use it to show that light reflects off a surface at equal angles. To set it up, you put in boundary conditions, ...
knzhou's user avatar
  • 103k