2010/01/04 by P Balseiro, P. Balseiro, J. C. Marrero +5
Engineering · Mathematics · Physics and Astronomy · #Algebra over a field #Construct (python library) #Control and Dynamics of Mobile Robots #Control and Stability of Dynamical Systems #Dissipative system #Homotopy and Cohomology in Algebraic Topology #Linear system #Nonlinear system #Variety (cybernetics) #math-ph #math.MP #msc:37J60. #msc:70F25 #msc:70G45 #msc:70H20
paper · pdf · doi:10.1088/0951-7715/23/8/006
30 pages, 3 figures
arxiv created 2010/01/04 · openalex publication_date 2010/07/02 · arxiv updated 2015/05/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In this paper, we construct Hamilton–Jacobi equations for a large variety of mechanical systems (nonholonomic systems subjected to linear or affine constraints, dissipative systems subjected to external forces, time-dependent mechanical systems etc). We recover all these, in principle, different cases, using a unified framework based on skew-symmetric algebroids with a distinguished 1-cocycle. Several examples illustrate the theory.