Contact Hamiltonian mechanics.pdfVIP

Annals of Physics 376 (2017) 17–39 Contents lists available at ScienceDirect Annals of Physics journal homepage: /locate/aop Contact Hamiltonian mechanics Alessandro Bravetti a,?, Hans Cruz b, Diego Tapias c a Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, A. P. 70543, México, DF 04510, Mexico b Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A. P. 70543, México, DF 04510, Mexico c Facultad de Ciencias, Universidad Nacional Autónoma de México, A.P. 70543, México, DF 04510, Mexico article info Article history: Received 15 May 2016 Accepted 9 November 2016 Available online 15 November 2016 Keywords: Hamiltonian mechanics Dissipative systems Contact geometry abstract In this work we introduce contact Hamiltonian mechanics, an extension of symplectic Hamiltonian mechanics, and show that it is a natural candidate for a geometric description of non-dissipative and dissipative systems. For this purpose we review in detail the major features of standard symplectic Hamiltonian dynamics and show that all of them can be generalized to the contact case. ? 2016 Elsevier Inc. All rights reserved. 1. Introduction The Hamiltonian formulation of classical mechanics is a very useful tool for the description of mechanical systems due to its remarkable geometrical properties, and because it provides a natural way to extend the classical theory to the quantum context by means of standard quantization. However, this formulation exclusively describes isolated systems with reversible dynamics, while real systems are constantly in interaction with an environment that introduces the phenomena of dissipation and irreversibility. Therefore a major question is whether it is possible to construct a classical mechanical theory that not only contains all the advantages of the Hamiltonian formalism, but also takes into account the effects of the environment on the system. Several programmes have been proposed f