2009/12/29 by Jan L. Cieslinski, Jan L Cieśliński, Tomasz Nikiciuk · 80 citations
Engineering · Mathematics · Physics and Astronomy · #Class (philosophy) #Control and Dynamics of Mobile Robots #Control and Stability of Dynamical Systems #Dynamical system (definition) #Dynamical systems theory #Lagrangian #Linear dynamical system #Quantum chaos and dynamical systems #Simple (philosophy) #Square (algebra) #Variable (mathematics) #math-ph #math.MP #msc:02.30.Hq #msc:37C60 #msc:37E99. #msc:45.20.-d #msc:45.20.Jj #msc:70H03
paper · pdf · doi:10.1088/1751-8113/43/17/175205
published in Journal of Physics A Mathematical and Theoretical 43(17), 175205 (Institute of Physics) · 17 pages
arxiv created 2009/12/29 · openalex publication_date 2010/04/14 · arxiv updated 2015/05/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We present a direct approach to the construction of Lagrangians for a large class of one-dimensional dynamical systems with a simple dependence (monomial or polynomial) on the velocity. We rederive and generalize some recent results and find Lagrangian formulations which seem to be new. Some of the considered systems (e.g. motions with the friction proportional to the velocity and to the square of the velocity) admit infinite families of different explicit Lagrangian formulations.