2000 character limit reached
Contact variational integrators (1902.00436v4)
Published 1 Feb 2019 in math.NA, cs.NA, math-ph, and math.MP
Abstract: We present geometric numerical integrators for contact flows that stem from a discretization of Herglotz' variational principle. First we show that the resulting discrete map is a contact transformation and that any contact map can be derived from a variational principle. Then we discuss the backward error analysis of our variational integrators, including the construction of a modified Lagrangian. Throughout the paper we use the damped harmonic oscillator as a benchmark example to compare our integrators to their symplectic analogues.