Hamilton equations for Lagrangian systems on fibred manifolds, subjected to general non-holonomic constraints (i.e., not necessarily affine in the velocities) are studied. Conditions for existence of a non-holonomic Legendre transformation are discussed, and the corresponding formulas for constraint momenta and Hamiltonian are found.

We establish some cohomological bounds in D-module theory that are known in the holonomic case and folklore in general. The method rests on a generalization of the b-function lemma for non-holonomic D-modules.

The mobile platform described in this paper is a holonomic type robotic vehicle. It is designed for use as a slave system in the development of a fault-tolerant teleoperation test-bed system. Therefore, the vehicle itself has a fault-tolerant design. This paper reviews the previous designs of mobile platforms, introduces several conceptual designs and the final design. Initial component selecti...

Starting from a characterization of admissible Cheataev and vakonomic variations in a field theory with constraints we show how the so called parametrized variational calculus can help to derive the vakonomic and the non-holonomic field equations. We present an example in field theory where the non-holonomic method proved to be unphysical.

We consider mechanical systems with intermittent contact that are smooth and holonomic except at the instants of transition. Overall such systems can be nonholonomic in that the accessible configuration space can have larger dimension than the instantaneous motions allowed by the constraints. The known examples of such mechanical systems are also dissipative. By virtue of their non-holonomy and...

We present two classes of random walks restricted to the quarter plane whose generating function is not holonomic. The non-holonomy is established using the iterated kernel method, a recent variant of the kernel method. This adds evidence to a recent conjecture on combinatorial properties of walks with holonomic generating functions. The method also yields an asymptotic expression for the numbe...

A sequence of complex numbers is holonomic if it satisfies a linear recurrence with polynomial coefficients. A power series is holonomic if it satisfies a linear differential equation with polynomial coefficients, which is equivalent to its coefficient sequence being holonomic. It is well known that all algebraic power series are holonomic. We show that the analogous statement for sequences is ...