In this article we develop a theory of contact systems with nonholonomic constraints. We obtain the dynamics from Herglotz's variational principle, by restricting variations so that they satisfy prove can be obtained as projection unconstrained Hamiltonian vector field. Finally, construct bracket, which is an almost Jacobi bracket on space observables and provides 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...

A new framework to perturbative quantum gravity is proposed following the geometry of nonholonomic distributions on (pseudo) Riemannian manifolds. There are considered such distributions and adapted connections, also completely defined by a metric structure, when gravitational models with infinite many couplings reduce to two–loop renormalizable effective actions. We use a key result from our p...

This paper addresses formulation of stabilizability and motion tracking conditions for mechanical systems from the point of view of constraints put on them. We present a new classification of constraints, which includes nonholonomic constraints that arise in both mechanics and control. Based on our classification we develop kinematic and dynamic control models of systems subjected to these cons...

We address the problem of motion planning for nonholonomic cooperating mobile robots manipulating and transporting objects while holding them in a stable grasp. We present a general approach for solving optimal control problems based on the calculus of variations. We specialize this approach to solving the motion planning problem and obtaining trajectories and actuator forces/torques for any ma...

We consider the fractional generalization of nonholonomic constraints defined by equations with fractional derivatives and provide some examples. The corresponding equations of motion are derived using variational principle. We prove that fractional constraints can be used to describe the evolution of dynamical systems in which some coordinates and velocities are related to velocities through a...

School of Mechanical Engineering Georgia Institute of Technology Atlanta, Georgia 30332 This paper describes a new technique for deriving dynamic equations of motion for serial chain and tree topology mechanisms with common nonholonomic constraints. For each type of nonholonomic constraint, the Boltzmann-Hamel equations produce a concise set of dynamic equations. These equations are similar to ...