29 citations · 140 across the 19 of their papers we have counts for
20 papers
Euler's elastica in nonlocal theory of elasticity
Vasyl Kovalchuk, Ewa Eliza Rożko, Barbara Gołubowska
A generalization of the Euler's elastic problem, i.e., finding a stationary configuration (planar elastica) of the Bernoulli's thin ideal elastic rod with boundary conditions defin…
Mechanics of Incompressible Test Bodies Moving in Riemannian Spaces
Vasyl Kovalchuk, Barbara Gołubowska, Ewa Eliza Rożko
In the present paper we have discussed the mechanics of incompressible test bodies moving in Riemannian spaces with non-trivial curvature tensors. For Hamilton's equations of motio…
Mechanics of the Infinitesimal Gyroscopes on the Mylar Balloons and Their Action-Angle Analysis
Vasyl Kovalchuk, Ivailo M. Mladenov
Here we apply the general scheme for description of the mechanics of infinitesimal bodies in the Riemannian spaces to the examples of geodetic and non-geodetic (for two different m…
Quantized Mechanics of Affinely-Rigid Bodies
Jan Jerzy Sławianowski, Vasyl Kovalchuk, Barbara Gołubowska +2
In this paper we develope the main ideas of the quantized version of affinely-rigid (homogeneously deformable) motion. We base our consideration on the usual Schrödinger formulatio…
Space-time as a structured relativistic continuum
Jan Jerzy Sławianowski, Vasyl Kovalchuk, Barbara Gołubowska +2
It is well known that there are various models of gravitation: the metrical Hilbert-Einstein theory, a wide class of intrinsically Lorentz-invariant tetrad theories (of course, gen…
Constraints and symmetry in mechanics of affine motion
Jan Jerzy Sławianowski, Barbara Gołubowska, Vasyl Kovalchuk
The aim of this paper is to perform a deeper geometric analysis of problems appearing in dynamics of affinely rigid bodies. First of all we present a geometric interpretation of th…
Generalized Weyl-Wigner-Moyal Formalism and Topological Groups
J. J. Sławianowski, V. Kovalchuk, A. Martens +2
Discussed are some geometric aspects of the phase space formalism in quantum mechanics in the sense of Weyl, Wigner, Moyal and Ville. We analyze the relationship between this forma…
Affine Bodies Revisited. Constraints, Symmetry, Analytical Methods and Some Perspectives
J. J. Sławianowski, B. Gołubowska, E. E. Rożko +3
The purpose of this publication is to derive and discuss equations of motion of affinely rigid (homogeneously deformable) body moving in Euclidean space of general dimension . O…
Mechanics of Systems of Affine Bodies. Geometric Foundations and Applications in Dynamics of Structured Media
Jan Jerzy Sławianowski, Vasyl Kovalchuk, Agnieszka Martens +2
In the present paper we investigate the mechanics of systems of affinely-rigid bodies, i.e., bodies rigid in the sense of affine geometry. Certain physical applications are possibl…
Quasiclassical and Quantum Systems of Angular Momentum. Part II. Quantum Mechanics on Lie Groups and Methods of Group Algebras
J. J. Sławianowski, V. Kovalchuk, A. Martens +2
In Part I of this series we presented the general ideas of applying group-algebraic methods for describing quantum systems. The treatment was there very "ascetic" in that only the…
Quasiclassical and Quantum Systems of Angular Momentum. Part I. Group Algebras as a Framework for Quantum-Mechanical Models with Symmetries
J. J. Sławianowski, V. Kovalchuk, A. Martens +2
We use the mathematical structure of group algebras and -algebras for describing certain problems concerning the quantum dynamics of systems of angular momenta, including al…
Quasiclassical and Quantum Systems of Angular Momentum. Part III. Group Algebra of , Quantum Angular Momentum and Quasiclassical Asymptotics
J. J. Sławianowski, V. Kovalchuk, A. Martens +2
This is the third part of our series "Quasiclassical and Quantum Systems of Angular Momentum". In two previous parts we have discussed the methods of group algebras in formulation…
On Classical Dynamics of Affinely-Rigid Bodies Subject to the Kirchhoff-Love Constraints
Vasyl Kovalchuk
In this article we consider the affinely-rigid body moving in the three-dimensional physical space and subject to the Kirchhoff-Love constraints, i.e., while it deforms homogeneous…
Symmetries and geometrically implied nonlinearities in mechanics and field theory
Jan Jerzy Sławianowski, Vasyl Kovalchuk
Discussed is relationship between nonlinearity and symmetry of dynamical models. The special stress is laid on essential, non-perturbative nonlinearity, when none linear background…
Classical models of affinely-rigid bodies with "thickness" in degenerate dimension
Vasyl Kovalchuk, Ewa Eliza Rożko
The special interest is devoted to such situations when the material space of our object with affine degrees of freedom has generally lower dimension than the one of the physical s…
Quantized excitations of internal affine modes and their influence on Raman spectra
J. J. Sławianowski, V. Kovalchuk, B. Gołubowska +2
Discussed is the structure of classical and quantum excitations of internal degrees of freedom of multiparticle objects like molecules, fullerens, atomic nuclei, etc. Basing on som…
Schrödinger and related equations as Hamiltonian systems, manifolds of second-order tensors and new ideas of nonlinearity in quantum mechanics
J. J. Sławianowski, V. Kovalchuk
Considered is the Schrödinger equation in a finite-dimensional space as an equation of mathematical physics derivable from the variational principle and treatable in terms of the L…
Dynamical systems with internal degrees of freedom in non-Euclidean spaces
J. J. Sławianowski, V. Kovalchuk, B. Gołubowska +2
Presented is description of kinematics and dynamics of material points with internal degrees of freedom moving in a Riemannian manifold. The models of internal degrees of freedom w…
Affine symmetry in mechanics of collective and internal modes. Part II. Quantum models
J. J. Sławianowski, V. Kovalchuk, A. Sławianowska +4
Discussed is the quantized version of the classical description of collective and internal affine modes as developed in Part I. We perform the Schrödinger quantization and reduce e…
Affine symmetry in mechanics of collective and internal modes. Part I. Classical models
J. J. Sławianowski, V. Kovalchuk, A. Sławianowska +4
Discussed is a model of collective and internal degrees of freedom with kinematics based on affine group and its subgroups. The main novelty in comparison with the previous attempt…