2000/04/13 by Xavier Gracia, Xavier Gràcia, Jesús Marín‐Solano +6
Engineering · Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Control and Dynamics of Mobile Robots #Dynamics and Control of Mechanical Systems #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.math-ph/0004019
LaTex file, 24 pages
arxiv created 2000/04/13 · openalex publication_date 2000/04/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a geometric description of variational principles in mechanics, with special attention to constrained systems. For the general case of nonholonomic constraints, a unified variational approach is given, and the equations of motion of both vakonomic and nonholonomic frameworks are obtained. We study specifically the existence of infinitesimal variations in both cases. When the constraints are integrable, both formalisms are compared and it is proved that they coincide. As examples, we give geometric formulations of the equations of motion for the case of optimal control and for vakonomic and nonholonomic mechanics with constraints linear in the velocities.