Contact variational integrators. (10th October 2019)

• Record Type: Journal Article
• Authors: Vermeeren, Mats; Bravetti, Alessandro; Seri, Marcello
• Is Part Of: Journal of physics. Volume 52:Number 44(2019)
• Publication Date: 2019-10-10
• Subjects: contact geometry -- geometric integrators -- Herglotz' variational principle; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/ab4767
• Languages: English
• ISSNs: 1751-8113

Abstract

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.