Some remarks about the complete integrability in the sense of Arnold-Liouville.
Given a Hilbert space with a Borel probability measure , we prove the -dissipativity in of a Kolmogorov operator that is a perturbation, not necessarily of gradient type, of an Ornstein-Uhlenbeck operator.
We associate to a dynamic equation three different connections and then we consider the meaning of the vanishing of their curvatures. Some peculiarities of the case of autonomous dynamic equation polynomial in the velocities are pointed out. Finally, using the so-called Helmholtz conditions, we investigate a particular example.
There exist many examples of closed kinematical chains which have a freedom of motion, but there are very few systematical results in this direction. This paper is devoted to the systematical treatment of 4-parametric closed kinematical chains and we show that the so called Bennet’s mechanism is essentially the only 4-parametric closed kinematical chain which has the freedom of motion. According to [3] this question is connected with the problem of existence of asymptotic geodesic lines on robot-manipulators...
The homogeneity properties of two different families of geometric objects playing a crutial role in the non-autonomous first-order dynamics - semisprays and dynamical connections on - are studied. A natural correspondence between sprays and a special class of homogeneous connections is presented.