Abstract
In this chapter we present the basic facts about the underlying structure of classical Hamiltonian mechanics and in particular statistical Hamiltonian mechanics. The theory is formulated in the frame of Poisson geometry and presymplectic geometry. On the level of statistical Hamiltonian mechanics we introduce the language and notions familiar from the quantum level in order to further unify both theories. In particular we consider such issues as Hamiltonian representation of variational problems of arbitrary order as well as the reduction of Poisson bi-vectors on submanifolds, important for further separability theory.
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Błaszak, M. (2019). Classical Hamiltonian Mechanics. In: Quantum versus Classical Mechanics and Integrability Problems. Springer, Cham. https://doi.org/10.1007/978-3-030-18379-0_3
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DOI: https://doi.org/10.1007/978-3-030-18379-0_3
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