All linearly damped Newton equations of a certain broad class are shown to fit a contact-geometry framework, which yields new higher-order geometric integrators with derived error estimates, tested on Kepler, spin-orbit, and Lane-Emden problems.
New contributions to the Hamiltonian and Lagrangian contact formalisms for dissipative mechanical systems and their symmetries
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abstract
We provide new insights into the contact Hamiltonian and Lagrangian formulations of dissipative mechanical systems. In particular, we state a new form of the contact dynamical equations, and we review two recently presented Lagrangian formalisms, studying their equivalence. We define several kinds of symmetries for contact dynamical systems, as well as the notion of dissipation laws, prove a dissipation theorem and give a way to construct conserved quantities. Some well-known examples of dissipative systems are discussed.
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Numerical integration in celestial mechanics: a case for contact geometry
All linearly damped Newton equations of a certain broad class are shown to fit a contact-geometry framework, which yields new higher-order geometric integrators with derived error estimates, tested on Kepler, spin-orbit, and Lane-Emden problems.