Hamilton–Jacobi formalism for geodesics and geodesic deviations
Copyright policy )Hamilton–Jacobi formalism for geodesics and geodesic deviations
A formalism of integrating the equations of geodesics and of geodesic deviation is examined based upon the Hamilton–Jacobi equation for geodesics. The latter equation has been extended to the case of geodesic deviation and theorems analogous to Jacobi’s theorem on the complete integral has been proved. As a result, a straightforward algorithm of integrating the geodesic deviation equations on Riemannian (or pseudo-Riemannian) manifolds is obtained.
- University of Warsaw Poland
equations of geodesics, Jacobi's theorem, Hamilton-Jacobi equations in mechanics, Hamilton-Jacobi equation, Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems, complete integral, geodesic deviation
equations of geodesics, Jacobi's theorem, Hamilton-Jacobi equations in mechanics, Hamilton-Jacobi equation, Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems, complete integral, geodesic deviation
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