Contact Algorithms for Contact Dynamical Systems (Journal of Computational Mathematics, 1998)
In this paper, we develop a general way to construct contact algorithms for contact dynamical systems. Such an algorithm requires the corresponding step-transition map preserve the contact structure of the underlying contact phase space. The constructions are based on the correspondence between the contact geometry of ${\bf R}^{2n+1}$ and the conic symplectic one of ${\bf R}^{2n+2}$ and therefore, the algorithms are derived naturally from the symplectic algorithms of Hamiltonian systems.
Keywords: Contact algorithms; contact systems; conic symplectic geometry; generating functions.