Physics 70 Principle of Least Action (3 of 27) Principle of Least Action & Energy Equation

We will understand The Principle of Least Action by studying the Conservation of Energy Equation.

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[pharaoh]

Sooo. A straight line from T0 to Tf would NOT be the path of least action because....?
Perhaps: Since here is a gain in potential energy as a result of height gain, there must also be an equivalent loss of Ke in velocity: Thus ▲Ke - ▲Pe equals Zero for Least Action over any time interval??

[andrewtaylor]

There seems to be an underlying assumption in the discussion that the path of least action is also the shortest path. You state that alternative paths are longer and must have higher velocity. But I can draw an alternative path that is shorter: a straight line between the two points. That path does not have to have higher velocity.

[darthkenobi]

could you please make videos about field equation and other cosmologic stuffs

[theultimatereductionist]

Let me rewrite Conservation of Energy equation
(KE(f)-KE(0)) + (PE(f)-PE(0)) + (Elost - W) = 0
So, the first two terms are still just a SUM of average KE & PE, not a difference.
i.e. Integral of ( KE(t) + PE(t) ) dt, not the action S = Integral of ( KE(t) - PE(t) ) dt
So I still do not understand how we get a minimum for S.

[lawrencehamachili]

i have a question in science on lenses

[aqeelshah]

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