Related papers: Equations of Motion of Systems with Internal Angul…
We present an algorithm for constructing analytically approximate integrals of motion in simple time periodic Hamiltonians of the form $H=H_0+ \varepsilon H_i$, where $\varepsilon$ is a perturbation parameter. We apply our algorithm in a…
Starting from the classical Newton's second law which, according to our assumption, is valid in any instantaneous inertial rest frame of body that moves in Minkowskian space-time we get the relativistic equation of motion…
We propose the deterministic dynamics of a free particle in a physical vacuum, which is considered as a discrete (quantum) medium. The motion of the particle is studied taking into account its interactions with the medium. It is assumed…
The angular motion of a few-body system is described with global vectors which depend on the positions of the particles. The previous study using a single global vector is extended to make it possible to describe both natural and unnatural…
We develop a geometric formulation of fluid dynamics, valid on arbitrary Riemannian manifolds, that regards the momentum-flux and stress tensors as 1-form valued 2-forms, and their divergence as a covariant exterior derivative. We review…
The motion of a rigid body is described in Classical Mechanics with the venerable Euler's equations which are based on the assumption that the relative distances among the constituent particles are fixed in time. Real bodies, however,…
In this paper we derive the equations of motion for nonholonomic systems subject to inequality constraints, both, in continuous-time and discrete-time. The last is done by discretizing the continuous time-variational principle which defined…
The solution of a momentum conservation equation for the gas and liquid stream in the flowing element is obtained on the basis of the modern approach to a problem on contact interaction of bodies and mediums. A flowing element, system are:…
The Fluctuation Theorems are a group of exact relations that remain valid irrespective of how far the system has been driven away from equilibrium. Other than having practical applications, like determination of equilibrium free energy…
Due to the processes that occur during the functioning of modern electromechanical systems, these systems can be considered complex nonlinear dynamic systems from the point of view of the theory of dynamic systems. The movement of such…
The purpose of the dynamics of moving systems is to search for the mathematical model that describes the link between the resultant applied force, that is the cause, and the speed of system that is the effect. This mathematical link…
We consider the exchange of spin and orbital angular momenta between a circularly polarized Laguerre-Gaussian beam of light and a single atom trapped in a two-dimensional harmonic potential. The radiation field is treated classically but…
The motion of a neutral atom endowed with a magnetic moment interacting with the magnetic field is determined from the Ehrenfest-like equations of motion. These equations for the average values of the translational and spin degrees of…
The purpose of this paper is to derive the dynamical equations for the period vectors of a periodic system under constant external stress. The explicit starting point is Newton's second law applied to halves of the system. Later statistics…
The symmetric tensor energy-impulse of interaction of collective of electric charges with an electromagnetic field is received. A system of covariant energy and momentum conservation equations or a system of equations for the collective…
We treat the classical dynamics of the hydrogen atom in perpendicular electric and magnetic fields as a celestial mechanics problem. By expressing the Hamiltonian in appropriate action-angle variables, we separate the different time scales…
We study a noncommutative deformation of general relativity where the gravitational field is described by a matrix-valued symmetric two-tensor field. The equations of motion are derived in the framework of this new theory by varying a…
This paper investigates the possibility of the motion control of a ball with a pendulum mechanism with non-holonomic constraints using gaits - the simplest motions such as acceleration and deceleration during the motion in a straight line,…
A method to study the topology of the integral manifolds basing on their projections to some other manifold of lower dimension is proposed. These projections are called the regions of possible motion and in mechanical systems arise in a…
The Hamiltonian formulation of the motion of a spinning relativistic particle in an external electromagnetic field is considered. The approach is based on the introduction of new coordinates and their conjugated momenta to describe the spin…