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The noncommutativity concept has wide range of applications in physical and mathematical theories. Noncommutativity in the position-time coordinates concerns the microscale structure of space-time. the noncommutativity is an intrinsic…
We model the instantaneous power applied by a cyclist on a velodrome -- for individual pursuits and other individual time trials -- taking into account its straights, circular arcs, and connecting transition curves. The forces opposing the…
In this work, the orbital evolution of these objects that are located in the geostationary orbit (GEO) is analyzed. Knowing this, the possibility of using a solar sail is considered to help to clean the space environment. The main natural…
In this paper we suggest an approach to analyse the motion of a test particle in the spacetime of a global monopole within a $f(R)$-like modified gravity. The field equations are written in a more simplified form in terms of…
A model of the gravitational dipole is proposed in a close analogy to that of the global monopole. The physical properties and the range of validity of the model are examined as is the motion of test particles in the dipole background. It…
We study a classical multiparticle system (such as Toda lattice) whose dynamics we intend to control by forces applied to few particles of the system. Various problem settings, typical for control theory are posed for this model; among…
The forced soliton equation is the starting point for semiclassical computations with solitons away from the small momentum transfer regime. This paper develops necessary analytical and numerical tools for analyzing solutions to the forced…
We deal with direct and inverse problems of the calculus of variations on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we give a general form for a variational functional to…
The dynamics of pseudo-classical spinning particles in spacetime of gravitational plane waves of general polarization and harmonic profile is studied. The resulting equations of motion are solved exactly and the results are compared with…
We study the motion of a particle in a particular magnetic field configuration both classically and quantum mechanically. For flux-free radially symmetric magnetic fields defined on circular regions, we establish that particle escape speeds…
The solutions of the classical equations of motion on a periodic lattice are found which correspond to abelian single and double Dirac sheets. These solutions exist also in non--abelian theories. Possible applications of these solutions to…
Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi--particle dynamical system by finding polynomial solutions of a partial differential equations is…
The definitions and some basic properties of the linear transports along paths in vector bundles and the normal frames for them are recalled. The formalism is specified on line bundles and applied to a geometrical description of the…
We formulate symmetric versions of classical variational principles. Within the framework of non-smooth critical point theory, we detect Palais-Smale sequences with additional second order and symmetry information. We discuss applications…
We compare the quantum and the classical description of the two-dimensional motion of electrons subjected to a perpendicular magnetic field and a one-dimensional lateral superlattice defined by spatially periodic magnetic and electric…
Problems involving rolling without slipping or no sideways skidding, to name a few, introduce velocity-dependent constraints that can be efficiently treated by the method of Lagrange multipliers in the Lagrangian formulation of the…
The general theory for electric current multipoles appearing at the motion of magnetic dipoles and change in these values or orientation has been suggested. Static multipoles, including an anapole, have been studied in detail.
We first review the application of Dirac's method to the dynamics of a classical particle constrained to a circle and its subsequent quantization. Then, we extend the analysis to a particle constrained to move on an ellipse. Particularly,…
In recent work, it was shown that elasticity theory can break down in amorphous solids subjected to nonuniform {\em static} loads. The elastic fields are screened by geometric dipoles; these stem from gradients of the quadrupole field…
A unified approach to the study of classical and quantum spin in external fields is developed. Understanding the dynamics of particles with spin and dipole moments in arbitrary gravitational, inertial and electromagnetic fields is important…