0
$\begingroup$

I understand that the equations appear to permit paths of maximal action, but is there any real physical case where this actually occurs? Would it not be more sensible to refer to this as the Principal of Least Action as most laypeople would call it?

My instincts would say that paths of least action were attractive stationary points and paths of maximal action were unstable/repulsive fixed points but I am not sure how to express/check this mathematically.

Improve this question
$\endgroup$
2
  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/907/2451 , physics.stackexchange.com/q/144356/2451 , physics.stackexchange.com/q/122486/2451 and links therein. $\endgroup$
    – Qmechanic ♦
    Commented Jan 30, 2023 at 10:08
  • 1
    $\begingroup$ There are indeed cases such that the true trajectory corresponds to a maximum of Hamilton's action. It depends on the type of potential. For simplicity: let there be the following cases for potential as a function of distance $r$: ..., $r^{-2}$, $r^{-1}$, $r^0$, $r^1$, $r^2$, $r^3$, ... When the potential increases with cube (or larger) of the position coordinate then the true trajectory corresponds to a maximum of Hamilton's action. For all potentials where the power is 1 or lower: minimum of Hamilton's action. It's just that cases with potential proportional to cube (and larger) are rare. $\endgroup$
    – Cleonis
    Commented Jan 30, 2023 at 16:31

0

Reset to default