General framework for nonholonomic mechanics: Nonholonomic systems on Lie affgebroids

A General Framework for Nonholonomic Mechanics: Nonholonomic Systems on Lie Affgebroids

This paper presents a geometric description of Lagrangian and Hamiltonian systems on Lie affgebroids subject to affine nonholonomic constraints. We define the notion of nonholonomically constrained system, and characterize regularity conditions that guarantee that the dynamics of the system can be obtained as a suitable projection of the unconstrained dynamics. It is shown that one can define a...

Discrete Nonholonomic Lagrangian Systems on Lie Groupoids

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 ...

Nonholonomic Lagrangian Systems on Lie Algebroids

This paper presents a geometric description on Lie algebroids of Lagrangian systems subject to nonholonomic constraints. The Lie algebroid framework provides a natural generalization of classical tangent bundle geometry. We define the notion of nonholonomically constrained system, and characterize regularity conditions that guarantee that the dynamics of the system can be obtained as a suitable...

Discrete Nonholonomic LL Systems on Lie Groups

This papers studies discrete nonholonomic mechanical systems whose configuration space is a Lie group G Assuming that the discrete Lagrangian and constraints are left-invariant, the discrete Euler–Lagrange equations are reduced to the discrete Euler–Poincaré–Suslov equations. The dynamics associated with the discrete Euler–Poincaré–Suslov equations is shown to evolve on a subvariety of the Lie ...

Nonholonomic Flows on Lie Groups