Seminar

Geometric Mechanics and Control Seminar

An introduction to contact Hamiltonian systems

Speaker:  Manuel de León (ICMAT-CSIC & Real Academia de Ciencias Exactas, Físicas y Naturales)
Date:  Friday, 22 January 2021 - 16:00
Place:  Online - zoom.us/j/93006808687?pwd=THpXbzhXTGJJY29KeXQxRTUvaGN1QT09 (ID: 930 0680 8687; Access code: 659820)

Abstract:
The aim of this talk is to introduce contact Hamiltonian systems, which unlike the most common ones in symplectic mechanics, lead to dissipated quantities. We will show how in the extended phase space $T^*Q imes mathbb{R}$ there is a canonical contact structure that allows to obtain the hamiltonian dynamics (hamiltonian vector field and evolution field). In the lagrangian case, given a regular lagrangian, we will have two different dynamics on the extended velocity space $TQ imes mathbb{R}$, one to describe a time-dependent system, the other for a lagrangian contact system, depending on the geometry used. We will also make a quick review of a number of recent results obtained in the context of this type of Hamiltonian systems.