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Non-standard Construction of Hamiltonian Structures and of the Hamilton-Jacobi equation

M. Herrera·S. A. Hojman
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Abstract

Examples of non-standard construction of Hamiltonian structures for dynamical systems and the respective Hamilton-Jacobi (H-J) equations, without using Lagrangians, are presented. Alternative H-J equations for Euler top are explicitly exhibited and solved. We demonstrate that some stability criterion, relating the slope of a Casimir function parametrized by the Lagrange multiplier to critical point type, depends on the used Hamiltonian structure and it is inadequate for this reason.

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M. Herrera, S. A. Hojman. 2000-08-10. Non-standard Construction of Hamiltonian Structures and of the Hamilton-Jacobi equation. https://arxiv.org/abs/math-ph/0008019

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