Contact variational integrators

Vermeeren, M., Bravetti, A. & Seri, M., 10-Oct-2019, In : Journal of Physics A: Mathematical and Theoretical. 55, 44, 27 p., 445206.

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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. Surprisingly, this construction presents some interesting simplifications compared to the corresponding construction for symplectic systems. Throughout the paper we use the damped harmonic oscillator as a benchmark example to compare our integrators to their symplectic analogues.
Original languageEnglish
Article number445206
Number of pages27
JournalJournal of Physics A: Mathematical and Theoretical
Issue number44
Publication statusPublished - 10-Oct-2019


  • math.NA, math-ph, math.MP

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