4 citations · 8 across the 10 of their papers we have counts for
11 papers
Application of Lagrangian mechanics equations for finding of the minimum distance between smooth submanifolds in N-dimensional Euclidean space -- Part II
Stanislav S. Zub, Sergiy I. Zub, Vladimir V. Semenov
The method of finding the minimal distance between smooth non crossing submanifolds in N-dimensional Euclidean space are presented. It based on solution of the equations that descr…
Quaternions in Hamiltonian dynamics of a rigid body -- Part III. Asymmetric Top in the Orbitron
Stanislav S. Zub, Sergiy I. Zub
The Poisson structure in the quaternion variables was proposed for asymmetric top in the external axially symmetric magnetic field. For that model of interaction the motion equatio…
Quaternions in Hamiltonian dynamics of a rigid body -- Part II. Relation of canonical Poisson and Lie-Poisson structures
Stanislav S. Zub, Sergiy I. Zub
It was proposed the Lie group such that symplectic structure of orbits of co-adjoint representation of the group is revealed symplectic structure of a rigid body dynamics in quater…
Quaternions in Hamiltonian dynamics of a rigid body -- Part I
Stanislav S. Zub, Sergiy I. Zub
This paper showed that Poisson brackets in quaternion variables can be obtained directly from canonical Poisson brackets on cotangent bundle of (or ) endowed by cano…
Hamiltonian dynamics of a symmetric top in external fields having axial symmetry. Levitating Orbitron
Stanislav S. Zub, Sergiy I. Zub
The symmetric top is a special case of the general top, and canonical Poisson structure on is the common method of its description. This structure is invariant under the…
Reduction of T*SE(3) to the Poisson structure for a symmetric top
Stanislav S. Zub, Sergiy I. Zub
Symmetrical top is a special case of a general top. The canonical Poisson structure on T*SE(3) is the common method of its description. This Poisson structure is invariant under th…
Stability of Hamiltonian relative equilibria in symmetric magnetically confined rigid bodies
Lyudmila Grigoryeva, Juan-Pablo Ortega, Stanislav Zub
This work studies the symmetries, the associated momentum map, and relative equilibria of a mechanical system consisting of a small axisymmetric magnetic body-dipole in an also axi…
Orbitron. Part II. Magnetic levitation
Stanislav S. Zub
This paper devoted to proof the existence of stable quasi-periodic motions of the magnetic dipole that is under the action of the external magnetic field and homogeneous field of g…
Orbitron. Part I. Stable orbital motion of magnetic dipole in the field of permanent magnets
Stanislav S. Zub
The main aim of this work was to give constructive proof of stable orbital motions existence in the systems of bodies, which interact only by magnetic forces.
The Grid: Prospects for Application in Metrology
P. I. Neyezhmakov, S. I. Zub, S. S. Zub
Global system of distributing computing - Grid - created as reply for challenges, connected with the qualitative progress of complexity of experimental physical assemblies and info…
Research into Orbital Motion Stability in System of Two Magnetically Interacting Bodies
Stanislav Zub
The stability of the orbital motion of two long cylindrical magnets interacting exclusively with magnetic forces is described. To carry out analytical studies a model of magnetical…