Far Eastern Mathematical Journal

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Covariant hydrodynamics of Hamiltonian systems

Gudimenko A.I.

2021, issue 2, P. 166–179 DOI: https://doi.org/10.47910/FEMJ202114

Abstract

The theory of hydrodynamic reduction of non-autonomous Hamiltonian mechanics (V. Kozlov, 1983) is presented in the geometric formalism of bundles over the time axis R. In this formalism, time is one of the coordinates, not a parameter; the connections describe reference frames and velocity fields of mechanical systems. The equations of the theory are presented in a form that is invariant with respect to time-dependent coordinate transformations and the choice of reference frames.

Keywords: covariant formalism, time-dependent Hamiltonian mechanics, multidimensional hydrodynamics

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References

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