Numerical integration in celestial mechanics: a case for contact geometry

Abstract

Several dynamical systems of interest in celestial mechanics can be written in the form of a Newton equation with time-dependent damping, linear in the velocities. For instance, the modified Kepler problem, the spin-orbit model and the Lane-Emden equation all belong to such class. In this work we start an investigation of these models from the point of view of contact geometry. In particular we focus on the (contact) Hamiltonisation of these models and on the construction of the corresponding geometric integrators.

arXiv commentPublished in Celestial Mechanics and Dynamical Astronomy

References in corpus (13)

• Contact Hamiltonian Mechanics
• Explicit symplectic approximation of nonseparable Hamiltonians: algorithm and long time performance
• Contact Hamiltonian Systems
• Cosymplectic and contact structures to resolve time-dependent and dissipative hamiltonian systems
• New contributions to the Hamiltonian and Lagrangian contact formalisms for dissipative mechanical systems and their symmetries
• Contact manifolds and dissipation, classical and quantum
• Lagrangian method for solving Lane-Emden type equation arising in astrophysics on semi-infinite domains
• A contact geometry framework for field theories with dissipation
• Contact variational integrators
• From an Action Principle for Action-dependent Lagrangians toward non-conservative Gravity: accelerating Universe without dark energy
• An Action Principle for Action-dependent Lagrangians: toward an Action Principle to non-conservative systems
• Slimplectic Integrators: Variational Integrators for General Nonconservative Systems
• Hamiltonian formulation of the spin-orbit model with time-varying non-conservative forces

Cited by in corpus (8)

• Invariant measures for contact Hamiltonian systems: symplectic sandwiches with contact bread
• Nonequilibrium thermodynamic process with hysteresis and metastable states -- A contact Hamiltonian with unstable and stable segments of a Legendre submanifold
• Numerical integration of stochastic contact Hamiltonian systems via stochastic Herglotz variational principle
• Perturbation-theory informed integrators for cosmological simulations
• The flow method for the Baker-Campbell-Hausdorff formula: exact results
• New directions for contact integrators
• Discrete Gravity with Local Lorentz Invariance
• Geometric numerical integration of Liénard systems via a contact Hamiltonian approach