The coupled problem of a solid oscillating in a viscous fluid under the action of an elastic force.
The determination of the velocities after impact for the constrained bar problem.
The geometry of Newton's law and rigid systems
We start by formulating geometrically the Newton’s law for a classical free particle in terms of Riemannian geometry, as pattern for subsequent developments. For constrained systems we have intrinsic and extrinsic viewpoints, with respect to the environmental space. Multi–particle systems are modelled on -th products of the pattern model. We apply the above scheme to discrete rigid systems. We study the splitting of the tangent and cotangent environmental space into the three components of center...
The Kowalevski's top and the method of Syzygies
A new algorithm for finding separation coordinates is tested on the example of Kowalev ski’s top.
The Lagrange rigid body motion
We discuss the motion of the three-dimensional rigid body about a fixed point under the influence of gravity, more specifically from the point of view of its symplectic structures and its constants of the motion. An obvious symmetry reduces the problem to a Hamiltonian flow on a four-dimensional submanifold of ; they are the customary Euler-Poisson equations. This symplectic manifold can also be regarded as a coadjoint orbit of the Lie algebra of the semi-direct product group with its natural...
The Rigid Body Dynamics: Classical and Algebro-geometric Integration
The rigid body with two controls and the Brockett perturbation.
The spectral stability of the rigid body with three linear controls.
Three-parametric robot manipulators with parallel rotational axes
The paper deals with asymptotic motions of 3-parametric robot manipulators with parallel rotational axes. To describe them we use the theory of Lie groups and Lie algebras. An example of such motions are motions with the zero Coriolis accelerations. We will show that there are asymptotic motions with nonzero Coriolis accelerations. We introduce the notions of the Klein subspace, the Coriolis subspace and show their relation to asymptotic motions of robot manipulators. The asymptotic motions are...
Tools for verifying classical and quantum superintegrability.
Trägheits- und höhere Momente eines Massensystemes in Bezug auf Ebenen.
Two classical periodic problems on time scales.