I am now attempting to figure out how to calculate trajectories using the highly coveted "principle of least action". I apologize beforehand if this is more of a mathematical problem than a problem that needs to be placed under classical mechanics. I also apologize if I can't do the Latex quite right the first time around. I want to overview what I know so far so I can receive corrections for any conceptual or silly mistakes I have made along the way.(adsbygoogle = window.adsbygoogle || []).push({});

So here's basically what I was taught. The Lagrangian (L) is the difference between the kinetic and potential energy:

[tex]L=K.E-P.E[/tex]

The action (denoted S) is denoted:

[tex]\int\limits_{t_1}^{t_0}L\, dt[/tex]

The problem I am having is being able to distinguish why the calculus of variations must be used rather than simple maxima and minima from calculus 1.

So, here's the point of what I need: can somebody explain to me the following things:

1. Why normal maxima and minima cannot solve this type of problem.

2. What exactly is the calculus of variations and how does it solve this type of problem.

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# Woes With the Principle of Least Action.

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