Geometric, control and numerical aspects of nonholonomic systems / Jorge Cortés Monforte

... Contents: the first chapter presents the literature review (a large number of references and historical comments thorough all book should be pointed out especially). The second chapter surveys the necesary tools: tensor fields and differential forms, distributions and codistributions, Lie group actions, connections, Riemannian metrics, symplectic structures, Poisson manifolds and tangent bundle geometry. Variational principles together with symplectic and affine connection reformulations are presented in the third chapter, whereas the symmetries of nonholonomic systems are thoroughly classified in the fourth chapter. The fifth chapter is devoted to Chaplygin systems ... Three concluding chapters are the most instructive: they deal with constraints of variable rank, with integration theory including the discrete Lagrange-d’Alembert principle, and with controllability.

The following examples considered in the book are worth mentioning: a rolling disk, a ball on rotating table (consisting of rough and smooth pieces), a snakeboard model, a plate with knife edge, several classes of moving robots, and many others. (Zentralblatt)