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Hamilton-Jacobi theory for Hamiltonian and non-Hamiltonian systems

This work was done on the theme of the State Task No. AAAA-A20-120011690135-5

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  • A generalization of the Hamilton-Jacobi theory to arbitrary dynamical systems, including non-Hamiltonian ones, is considered. The generalized Hamilton-Jacobi theory is constructed as a theory of ensemble of identical systems moving in the configuration space and described by the continual equation of motion and the continuity equation. For Hamiltonian systems, the usual Hamilton-Jacobi equations naturally follow from this theory. The proposed formulation of the Hamilton-Jacobi theory, as the theory of ensemble, allows interpreting in a natural way the transition from quantum mechanics in the Schrödinger form to classical mechanics.

    Mathematics Subject Classification: Primary: 70H20, 70S05; Secondary: 37J05.


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