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Generalized Hamiltonian dynamics. (English) Zbl 1027.70503
Summary: Taking the Liouville theorem as a guiding principle, we propose a possible generalization of classical Hamiltonian dynamics to a three-dimensional phase space. The equation of motion involves two Hamiltonians and three canonical variables. The fact that the Euler equations for a rotator can be cast into his form suggests the potential usefulness of this formalism. In this article we study its general properties and the problem of quantization.

MSC:
70H99 Hamiltonian and Lagrangian mechanics
70H45 Constrained dynamics, Dirac’s theory of constraints
70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics
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