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Ling, Samson Cheuk Hin

In classical mechanics, the principle of least action states that an object’s motion minimizes the action, a fundamental scalar quantity related to its energy. Lagrangian mechanics, derived from the Hamiltonian principle, excels in predicting trajectories within conservative fields where forces depend solely on position. Nevertheless, traditional Lagrangian mechanics face limitations in handling nonconservative forces like friction or air drag. Recent breakthroughs in Dissipative Lagrangian mechanics have addressed this gap, especially in describing nonconservative forces. Our research extends this innovative formalism to Hamiltonian mechanics, emphasizing dissipation in dynamic systems. The primary focus lies in applying non-conservative Hamiltonian mechanics to compute dissipation for physical quantities such as energy and momentum in non-conservative systems. The study explores consequential alterations in Liouville’s theorem to describe the behavior of phase space volume under dissipation. In conventional Liouville’s theorem, the phase space volume remains constant over time. The new dissipative Hamiltonian mechanics enable the description of the change in phase space volume under dissipation. The results are validated by computational simulations to compare with classical examples like the damped harmonic oscillator and a falling ball with drag. Having established a non-conservative Hamiltonian formalism, our future goal aims to apply it to calculate dissipation resulting from gravitational waves in binary systems and address unresolved issues surrounding dissipation in physical systems.

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University of British Columbia. PHYS 449

Vancouver : University of British Columbia Library

10.14288/1.0448130

Science, Faculty of; Mathematics, Department of; Physics and Astronomy, Department of

Undergraduate

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