Related papers: Why do we use constants of motion while studying t…

This work investigates the dynamics of closed quantum systems in the Bloch vector representation using methods from rigid body dynamics and the theory of integrable systems. To this end, equations of motion for Bloch components are derived…

The Lagrangian, the Hamiltonian and the constant of motion of the gravitational attraction of two bodies when one of them has variable mass is considered. The relative and center of mass coordinates are not separated, and choosing the…

It is well-known that an electric charge under a uniform magnetic field has a bidimensional motion if its initial position and velocity are perpendicular to this magnetic field. Although some constants of motion, as the energy and angular…

We give an elementary derivation of the Montgomery phase formula for the motion of an Euler top, using only basic facts about the Euler equation and parallel transport on the 2-sphere (whose holonomy is seen to be responsible for the…

We develop the canonical formalism for a system of $N$ bodies in lineal gravity and obtain exact solutions to the equations of motion for N=2. The determining equation of the Hamiltonian is derived in the form of a transcendental equation,…

The diffusion in two dimensions of non-interacting active particles that follow an arbitrary motility pattern is considered for analysis. Accordingly, the transport equation is generalized to take into account an arbitrary distribution of…

A double pendulum subject to external torques is used as a model to study the stability of a planar manipulator with two links and two rotational driven joints. The hamiltonian equations of motion and the fixed points (stationary solutions)…

We study the symmetries enjoyed by the Newtonian equations of motion of the non-relativistic dark matter fluid coupled to gravity which give rise to the phenomenon of gravitational instability. We also discuss some consistency relations…

There are several formulations of the second law, and they may, in principle, have different domains of validity. Here a simple mathematical theorem is proven which serves as the most general basis for the second law, namely the Thomson…

There are two main reasons why relative equilibria of N point masses under the influence of Newton attraction are mathematically more interesting to study when space dimension is at least 4: On the one hand, in a higher dimensional space, a…

The torque on a moving electric or magnetic dipole in slow motion is deduced using the Lorentz transformation of the fields to first order in v/c. It is shown that the obtained equations are independent of the model adopted for the dipole,…

The stochastic dynamics of an active particle undergoing a constant speed and additionally driven by an overall fluctuating torque is investigated. The random torque forces are expressed by a stochastic differential equation for the angular…

In this paper we consider equations of motion for 2-body problem according to an observer close to one of the gravitational bodies. The influence of the Thomas precession of the observer's frame has an important role. The equations of…

The existence of vacuum fluctuations leads to reconsider the question of relativity of motion. The present article is devoted to this aim with a main line which can be formulated as follows: ``The principle of relativity of motion is…

We analyze the two-dimensional motion of a rigid body due to a constant torque generated by a force acting on the body parallel to the surface on which the body moves extending an old note of Ferris-Prabhu [Am. J. Phys. 38, 1356-1357…

The simple realistic model of the tippe top is considered. An averaged system of equations of motion is obtained in special evolutionary variables. Through the qualitative analysis of this system the general features of the motion of the…

In this paper we introduce a proposal for the kinematics of bodies in uniform circular motion. This model could contribute for the explanation of the two main problems of contemporary cosmology: dark matter and dark energy. We use one of…

From the mesoscopic point of view, a new concept of soft matching for mass points is proposed. Then a soft Lasso's approach to learn the soft dynamical equation for the physical mechanical relationship is proposed, too. Furthermore, a…

Transformation rules for coordinates, velocities and accelerations in accelerated reference frames are derived. A generalized approach of the special relativity is taken for a basis. A 7-dimensional space including projections of velocity…

We consider secular perturbations of nearly Keplerian two-body motion under a perturbing potential that can be approximated to sufficient accuracy by expanding it to second order in the coordinates. After averaging over time to obtain the…