This question already has an answer here:
- Is the principle of least action a boundary value or initial condition problem? 5 answers
- In the Principle of Least Action, how does a particle know where it will be in the future? 6 answers
- Why can we consider the endpoint fixed in the derivation of the Euler-Lagrange equation in mechanics? 2 answers
The stationary action principle states that a system evolves between a fixed initial and fixed final configuration in such a way that the action is stationary.
But isn't the final configuration what we usually try to predict? We start with some initial configuration and then try to figure out how the system will look like at a later point in time, i.e. the final configuration.
(I know that technically we can calculate the equations of motions using the Euler-Lagrange equation. These equations allow us to predict which final configuration is the right one for a given initial configuration. But I was wondering how this conceptually makes sense if we derive them by demanding that the final configuration needs to be specified in the first place.)