In this paper the notion of robot-manipulators in the Euclidean space is generalized to the case in a general homogeneous space with the Lie group of motions. Some kinematic subspaces of the Lie algebra (the subspaces of velocity operators, of Coriolis acceleration operators, asymptotic subspaces) are introduced and by them asymptotic and geodesic motions are described.
We establish the analytic non-integrability of the nonholonomic ellipsoidal rattleback model for a large class of parameter values. Our approach is based on the study of the monodromy group of the normal variational equations around a particular orbit. The imbedding of the equations of the heavy rigid body into the rattleback model is discussed.
* Partially supported by Grant MM523/95 with Ministry of Science and Technologies.In this paper the classical Kirchhoff case of motion of a rigid body in an infinite ideal fluid is considered. Then for the corresponding Hamiltonian system on the zero integral level, the KAM theory conditions are checked. In contrast to the known similar results, there exists a curve in the bifurcation diagram along which the Kolmogorov’s condition vanishes for certain values of the parameters.