How can differential equations describing a physical object's true spatial paths (orbits) be derived from the time-independent Jacobi-Maupertuis principle of least action? According to this, it is possible.
The time-independent version of Maupertuis' principle yields (Lanczos 1970, Landau and Lifshitz 1969) corresponding differential equations for the true spatial paths (orbits).
I guess I am looking for equations analogous to the Euler-Lagrange conditions, but for true spatial paths (orbits) instead of true trajectories as a function of time.
This PSE post is relevant, but is concerned with the derivation of equations of motion, whereas here I am concerned with the derivation of true spatial paths (orbits).