Abstract
The Hamilton-Jacobi theory is extended to include the case of Lagrangians involving higher-order time derivatives of the degrees of freedom. In particular, Jacobi’s theorem is generalized and proved in this case. By way of application, the Hamilton-Jacobi equation for a particle constrained to turn about a translating centre is set and solved, starting from an associated Lagrangian containing the second-order time derivatives of the particle position co-ordinates.
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