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.


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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