Linked Questions

14
votes
6answers
2k views

In the Principle of Least Action, how does a particle know where it will be in the future?

In his book on Classical Mechanics, Prof. Feynman asserts that it just does. But if this is really what happens (& if the Principle of Least Action is more fundamental than Newton's Laws), then ...
7
votes
3answers
3k views

What's the difference between “boundary value problems” and “initial value problems”?

Mathematically speaking, is there any essential difference between initial value problems and boundary value problems? The specification of the values of a function $f$ and the "velocities" $\frac{\...
2
votes
3answers
768 views

Is the path of stationary action unique? What are the physical implications of $L_{\dot{x}}=L_x$

Below, for any function $Q$ the notation $Q_x$ means $\frac{\partial Q}{\partial x}$, and $Q_{xx}$ means $\frac{\partial^2 Q}{\partial x^2}$. In physics, the trajectory of a particle is given by the ...

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