We formulate an approach to the geometry of Riemann–Cartan spaces provided with nonholonomic distributions defined by generic off-diagonal and nonsymmetric metrics inducing effective nonlinear and affine connections. Such geometries can be modelled by moving nonholonomic frames on (pseudo) Riemannian manifolds and describe various types of nonholonomic Einstein, Eisenhart–Moffat and Finsler–Lag...

We present a demonstrative application of the nonholonomic control method to a real physical system composed of two cold Cesium atoms. In particular, we show how to implement a CN OT quantum gate in this system by means of a controlled Stark field.

In our paper, we address the following question: “Which nonholonomic control systems are locally feedback equivalent to the canonical contact system on Jn(R;Rm )?” We provide easily checkable necessary and sufficient conditions, expressed in terms of the original system, for such a feedback transformation to exist. Moreover, our proofs exhibit a deep geometry of contact systems.

In this paper we examine a new class of five dimensional (5D) exact solutions in extra dimension gravity possessing Lie algebroid symmetry. The constructions provide a motivation for the theory of Clifford nonholonomic algebroids elaborated in Ref. [1]. Such Einstein–Dirac spacetimes are parametrized by generic off–diagonal metrics and nonholonomic frames (vielbeins) with associated nonlinear c...

We discuss an extension of the Hamilton–Jacobi theory to nonholonomic mechanics with a particular interest in its application to exactly integrating the equations of motion. We give an intrinsic proof of a nonholonomic analogue of the Hamilton–Jacobi theorem. Our intrinsic proof clarifies the difference from the conventional Hamilton–Jacobi theory for unconstrained systems. The proof also helps...

This paper continues the work of Koon and Marsden [1997b] that began the comparison of the Hamiltonian and Lagrangian formulations of nonholonomic systems. Because of the necessary replacement of conservation laws with the momentum equation, it is natural to let the value of momentum be a variable and for this reason it is natural to take a Poisson viewpoint. Some of this theory has been starte...

In this paper we incorporate dipolar potential fields used for nonholonomic navigation into a novel potential function designed for multi – robot navigation. The derived navigation function is suitable for navigation of multiple nonholonomic vehicles. A properly designed discontinuous feedback control law is applied to steer the nonholonomic vehicles. The derived closed form control scheme prov...

We analyze the behavior of redundant robots when the joint motion is generated by inverting task velocity commands through a kinematic control scheme. Depending on the chosen inversion scheme, the robot motion is subject to differential constraints that may or may not be integrable. Accordingly, we give a classification in terms of holonomic, partially nonholonomic, and completely nonholonomic ...