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arXiv · 2301.09355

Generalized virial theorem for contact Hamiltonian systems

Aritra Ghosh
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Abstract

We formulate and study a generalized virial theorem for contact Hamiltonian systems. Such systems describe mechanical systems in the presence of simple dissipative forces such as Rayleigh friction, or the vertical motion of a particle falling through a fluid (quadratic drag) under the action of constant gravity. We find a generalized virial theorem for contact Hamiltonian systems which is distinct from that obtained earlier for the symplectic case. The `contact' generalized virial theorem is shown to reduce to the earlier result on symplectic manifolds as a special case. Various examples of dissipative mechanical systems are discussed. We also formulate a generalized virial theorem in the contact Lagrangian framework.

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Aritra Ghosh. 2023-01-23. Generalized virial theorem for contact Hamiltonian systems. https://doi.org/10.1088/1751-8121/accfd3

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