We will discuss the so-called mixed endpoint conditions for variational problems with non-holonomic constraints given by form actions of order greater than one. We will present some results and discuss the inverse problem of Calculus of Variations.

P. A. Griffiths established the so-called mixed endpoint conditions for variational problems with non-holonomic constraints. We will present some results in this context and discuss the inverse problem of calculus of variations.

Chomsky and Schützenberger showed in 1963 that the sequence dL(n), which counts the number of words of a given length n in a regular language L, satisfies a linear recurrence relation with constant coefficients for n, i.e., it is C-finite. It follows that every sequence s(n) which satisfies a linear recurrence relation with constant coefficients can be represented as dL1 (n)− dL2 (n) for two re...

A robust finite-time control law is proposed for mobile manipulators with uncertain both kinematic and dynamic equations. Moreover, the following external disturbances are allowed to act on system: unstructured forces exerted end-effector, slip reaction affecting platform wheels, unknown friction coming from joints directly driven by actuators undesirable caused singular configurations. In orde...

We will discuss some new results for the inverse problem of Variational Calculus. We will consider problems with functionals given by action forms of order greater than one and subject to non-holonomic constraints.

The feedback control of a nonholonomic 3D floating vehicle is considered: namely the control objective is to drive a vehicle moving in 3D space to a given point and heading along a given line having as control inputs a 1D linear velocity (surge velocity) and a 2D angular one allowing the vehicle to rotate around any axis normal to the surge one. This kind of kinematic describes a large class of...

We study the Fourier-Mukai transform for holonomic D-modules on complex abelian varieties. Among other things, we show that the cohomology support loci of a holonomic D-module are finite unions of linear subvarieties, which go through points of finite order for objects of geometric origin; that the standard t-structure on the derived category of holonomic complexes corresponds, under the Fourie...

The dynamics of rigid bodies coupled by holonomic and non-holonomic constraints are formulated by the Newton Euler method employing a compact notation. The compact notation involves the use of two three by three matrices A and B and the totality of constraint vector C. The Lagrangian and Newton Euler methods are related for a one link rigid body in order to introduce the methodology of the pape...

In this paper we address the problem of planning the motion of a team of cooperating mobile robots subject to constraints on relative configuration imposed by the nature of the task they are executing. We model constraints between robots using a graph where each edge is associated with the interaction between two robots and describes a constraint on relative configurations. We develop a decentr...

The paper presents a simple, robust, and effective constraint enforcement scheme for rigid body dynamic simulation. The constraint enforcement scheme treats the constraint equations implicitly providing stability as well as accuracy in constrained dynamic problems. The method does not require ad-hoc problem dependent parameters. We describe the formulation of implicit constraint enforcement for...