Geometry Induced Adaptive Dissipation in Non Linear Contact Hamiltonian Systems Theory and Application to Duffing Oscillator

Vinesh Vijayan; R Sathishkumar; D Kaleeswaran

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arXiv · 2607.17055

Geometry Induced Adaptive Dissipation in Non Linear Contact Hamiltonian Systems Theory and Application to Duffing Oscillator

Vinesh Vijayan·R Sathishkumar·D Kaleeswaran

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Abstract

We develop a generalized contact Hamiltonian framework by extending canonical contact Hamiltonian mechanics to nonlinear dissipative systems through the replacement of the classical linear contact potential with a smooth nonlinear contact potential. The proposed formulation establishes a generalized energy dissipation law together with a structural characterization of admissible contact-induced damping, introducing effective contact dissipation as an intrinsic geometric measure of adaptive dissipation. As an application, a generalized contact Duffing oscillator is derived, in which dissipation emerges intrinsically from the contact geometry rather than being introduced phenomenologically. Numerical investigations of the generalized contact Duffing oscillator demonstrate that nonlinear contact geometry governs the effective dissipation and produces significant changes in the phase-space structure, energy decay, dynamical stability, and long-term nonlinear behavior. The proposed theory therefore provides a systematic geometric framework for constructing and analyzing nonlinear dissipative Hamiltonian systems within contact Hamiltonian mechanics.

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Vinesh Vijayan, R Sathishkumar, D Kaleeswaran. 2026-07-19. Geometry Induced Adaptive Dissipation in Non Linear Contact Hamiltonian Systems Theory and Application to Duffing Oscillator. https://arxiv.org/abs/2607.17055

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