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.

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© 1989 American Institute of Physics.
1989
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