29 citations · 67 across the 8 of their papers we have counts for
10 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…
Some aspects of affine motion and nonholonomic constraints. Two ways to describe homogeneously deformable bodies
Barbara Gołubowska
This paper has been inspired by ideas presented by V. V. Kozlov in his works [19, 20]. In this paper our goal is to carry out a thorough analysis of some geometric problems of the…
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…
Motion of test bodies with internal degrees of freedom in non-Euclidian spaces
J. J. Sławianowski, B. Gołubowska
Discussed is mechanics of objects with internal degrees of freedom in generally non-Euclidean spaces. Geometric peculiarities of the model are investigated detailly. Discussed are…
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…