We obtain the equations of motion for a Lagrangian dynamical system under nonholonomic constraints making use of the D’Alembert principle. We show that the Lagrange multipliers can be expressed in terms of the Poisson bracket of the Hamiltonian and the constraint. This appealing result greatly simplifies the derivation of the equations of motion. The existence of at least two conserved quantiti...

In this paper, the problem of localizing a nonholonomic vehicle moving in an unstructured environment is addressed by the design of a novel nonlinear observer, based on suitably processed optical information. The localization problem has been shown to be intrinsically nonlinear, indeed the linear approximation of the system has di erent structural properties than the original model. The propose...

We report on new applications of the Poincaré and Sundman timetransformations to the simulation of nonholonomic systems. These transformations are here applied to nonholonomic mechanical systems known to be Hamiltonizable (briefly, nonholonomic systems whose constrained mechanics are Hamiltonian after a suitable time reparameterization). We show how such an application permits the usage of vari...

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...

We consider a class of dynamical systems on a Lie group G with a leftinvariant metric and right-invariant nonholonomic constraints (so called LR systems) and show that, under a generic condition on the constraints, such systems can be regarded as generalized Chaplygin systems on the principle bundle G → Q = G/H , H being a Lie subgroup. In contrast to generic Chaplygin systems, the reductions o...

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...

For (2+2)–dimensional nonholonomic distributions, the physical information contained into a spacetime (pseudo) Riemannian metric can be encoded equivalently into new types of geometric structures and linear connections constructed as nonholonomic deformations of the Levi–Civita connection. Such deformations and induced geometric/physical objects are completely determined by a prescribed metric ...

Nonholonomic control is a candidate to nonlinear systems with path-dependant states. We investigate an underactuated flying micro-aerial-vehicle, the ionocraft, that requires nonholonomic in yaw-direction for complete attitude control. Deploying analytical law involves substantial engineering design and sensitive inaccuracy system model. With specific assumptions on assembly dynamics, we derive...

In this paper we study Chaplygin’s Reducibility Theorem and extend its applicability to nonholonomic systems with symmetry described by the Hamilton-Poincaré-d’Alembert equations in arbitrary degrees of freedom. As special cases we extract the extension of the Theorem to nonholonomic Chaplygin systems with nonabelian symmetry groups as well as Euler-Poincaré-Suslov systems in arbitrary degrees ...

The motion planning problem of a free-falling cat is investigated. Nonholonomicity arises in a free-falling cat subject to nonintegrable velocity constraints or nonintegrable conservation laws. When the total angular momentum is zero, the rotational motion of the cat subjects to nonholonomic constraints. The equation of dynamics of a free-falling cat is obtained by using the model of two symmet...