Finding geodesics joining given points
Finding a geodesic joining two given points in a complete path-connected Riemannian
manifold requires much more effort than determining a geodesic from initial data. This is …
manifold requires much more effort than determining a geodesic from initial data. This is …
Finding extremals of Lagrangian actions
Given a smooth m-manifold M, a smooth Lagrangian L: TM→ R and endpoints x 0, x T∈ M,
we look for an extremal x:[0, T]→ M of the action∫ 0 TL (x (t), x ̇ (t)) dt satisfying x (0)= x 0 …
we look for an extremal x:[0, T]→ M of the action∫ 0 TL (x (t), x ̇ (t)) dt satisfying x (0)= x 0 …