Reduction, Hamilton-Jacobi theory and discretization of mechanical systems with external forces

Speaker:  Asier López Gordón (ICMAT)
Date:  Friday, 01 April 2022 - 15:30
Online:   us06web.zoom.us/j/7555463367 (ID: 755 546 3367)

Abstract:

The description of numerous mechanical systems requires considering an external force together with the Lagrangian or the Hamiltonian, for instance, a dissipative force. Moreover,  a Chaplygin non-holonomic system is tantamount to a forced Lagrangian system without constraints. In this talk, I will show how some well-known results for conservative systems are naturally extended to forced systems in the framework of symplectic geometry. Regarding continuous systems, a Noether’s theorem, a generalization of the Symplectic point reduction theorem and a Hamilton-Jacobi theory will be presented. Additionally,  a discrete Hamilton-Jacobi theory and the notion of discrete Rayleigh systems will be introduced.

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