This paper studies the construction of geometric integrators for nonholonomic systems. We derive the nonholonomic discrete Euler-Lagrange equations in a setting which permits to deduce geometric integrators for continuous nonholonomic systems (reduced or not). The formalism is given in terms of Lie groupoids, specifying a discrete Lagrangian and a constraint submanifold on it. Additionally, it ...

The reduction and reconstruction of the dynamics of nonholonomic mechanical systems with symmetry are investigated. We have considered a more general framework of constrained hamiltonian systems since they appear in the reduction procedure. A reduction scheme in terms of the nonholonomic momentum mapping is developed. The reduction of the nonholonomic brackets is also discussed. The theory is i...

A geometric derivation of nonholonomic integrators is developed. It is based in the classical technique of generating functions adapted to the special features of nonholonomic systems. The theoretical methodology and the integrators obtained are different from the obtained in [12]. In the case of mechanical systems with linear constraints a family of geometric integrators preserving the nonholo...

Exploiting unique features of nonholonomic systems, innovative and advantageous mechanisms can be designed. We have proposed a nonholonomic manipulator which is a controllable n joint manipulator with only two actuators. In order to create its nonholonomic constraint, a special type of velocity transmission, called the nonholonomic gear, was developed. There are many possible alternatives for d...

When the generalized velocity of a mechanical system satis es an equality condition that cannot be written as an equivalent condition on the generalized position, the system is called a nonholonomic system [1, 2]. Nonholonomic condition may arise from constraints such as pure rolling of a wheel or from physical conservation laws such as the conservation of angular momentum of a free oating body...