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arXiv · 2504.00498

Dynamical Similarity in Higher-Order Classical Symplectic Systems

Callum Bell·David Sloan
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Abstract

Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a reduction process to be carried out, eliminating a single degree of freedom from the system, which we associate with an overall scale. This process of `contact reduction' leads to theories of a frictional nature, in which the physically-observable quantities form an autonomous subsystem, that evolves in a predictable manner. We demonstrate that this procedure has a natural generalisation to theories of higher order; detailed examples are provided, and physical implications discussed.

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Callum Bell, David Sloan. 2025-04-01. Dynamical Similarity in Higher-Order Classical Symplectic Systems. https://arxiv.org/abs/2504.00498

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