Finding trajectories that minimize the action

We have used the variational principle to determine if a given trajectory is realizable. We can also use the variational principle to find trajectories. Given a set of trajectories that are specified by a finite number of parameters, we can search the parameter space looking for the trajectory in the set that best approximates the real trajectory by finding one that minimizes the action. By choosing a good set of approximating functions we can get arbitrarily close to the real trajectory.

— Structure and Interpretation of Classical Mechanics

.

We have used the variational principle to determine if a given trajectory is realizable.

How?

— Me@2019-03-29 04:23:36 PM

.

Check if the action of that given trajectory is stationary or not.

— Me@2019-03-29 04:25:45 PM

.

.

2019.03.29 Friday (c) All rights reserved by ACHK