2014/11/12 by Viviana Alejandra Díaz, David Martı́n de Diego, Díaz, Viviana Alejandra +1
Engineering · Mathematics · Physics and Astronomy · #Control and Dynamics of Mobile Robots #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1411.3276
openalex publication_date 2014/11/12 · openalex created_date 2022/09/01 · openalex updated_date 2026/07/28
In this paper, we consider a generalization of variational calculus which\nallows us to consider in the same framework different cases of mechanical\nsystems, for instance, Lagrangian mechanics, Hamiltonian mechanics, systems\nsubjected to constraints, optimal control theory and so on. This generalized\nvariational calculus is based on two main notions: the tangent lift of curves\nand the notion of complete lift of a vector field. Both concepts are also\nadapted for the case of skew-symmetric algebroids, therefore, our formalism\neasily extends to the case of Lie algebroids and nonholonomic systems. Hence,\nthis framework automatically includes reduced mechanical systems subjected or\nnot to constraints. Finally, we show that our formalism can be used to tackle\nthe case of discrete mechanics, including reduced systems, systems subjected to\nconstraints and discrete optimal control theory.\n