2020/03/26 by Alexandre Anahory Simoes, David Martín de Diego, Manuel de León +1
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Contact Mechanics and Variational Inequalities #Contact geometry #Contact mechanics #Control and Stability of Dynamical Systems #Function (biology) #Integrator #Lagrangian #Lagrangian mechanics #Numerical methods for differential equations #Surface (topology) #Variational integrator #Variational principle #cs.NA #math-ph #math.MP #math.NA #msc:34C25 #msc:37E40 #msc:70K40
paper · pdf · doi:10.1007/s00332-021-09708-2
arxiv created 2020/03/26 · openalex created_date 2020/04/03 · openalex publication_date 2021/04/21 · arxiv updated 2021/05/05 · openalex updated_date 2026/08/05
In this paper, we continue the construction of variational integrators adapted to contact geometry started in \citeVBS, in particular, we introduce a discrete Herglotz Principle and the corresponding discrete Herglotz Equations for a discrete Lagrangian in the contact setting. This allows us to develop convenient numerical integrators for contact Lagrangian systems that are conformally contact by construction. The existence of an exact Lagrangian function is also discussed.