A geometric approach to the (generalized) Noether theorem for Hamiltonian systems on (non)-uniform q-contact manifolds

2026/08/06 by Manuel de León, Cristina Sardón, Xuefeng Zhao
Mathematics · Physics and Astronomy · #math.SG #math-ph #math.MP #msc:53C15 #msc:37J06 #msc:53D99

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arxiv created 2026/08/06 · arxiv updated 2026/08/07

Abstract

In this paper, we develop a unified Hamiltonian framework for dynamical systems with multiple independent dissipation channels based on q-contact geometry. As an application, we embed an elastoplastic damage model with two internal variables into the non-uniform 2-contact framework, explicitly construct the underlying geometric structure, derive the effective equations of motion, and validate the theoretical predictions through numerical simulations, which confirm the exponential dissipation law and the associated rescaled conserved quantity.

Citations

• Integration on q-Cosymplectic Manifolds
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• Eisenhart lifts and symmetries of time-dependent systems
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• Trans-Planckian particles and the quantization of time