相关论文: Circular orbits of a ball on a rotating conical tu…
Point vortices on a cylinder (periodic strip) are studied geometrically. The Hamiltonian formalism is developed, a non-existence theorem for relative equilibria is proved, equilibria are classified when all vorticities have the same sign,…
This paper is a review of the dynamics of a system of planets. It includes the study of averaged equations in both non-resonant and resonant systems and shows the great deal of situations in which the angle between the two semi-major axes…
An interesting physical phenomenon, which contradicts our common sense, is concerned with the dynamics of motion of a spinning ellipsoid in a non smooth surface. A hard-boiled egg spinning on a table with a rough surface is an example. In…
Numerical modelling of coherent spin relaxation in nanomagnets, formed by magnetic molecules of high spins, is accomplished. Such a coherent spin dynamics can be realized in the presence of a resonant electric circuit coupled to the magnet.…
Dynamic behavior of a weightless rod with a point mass sliding along the rod axis according to periodic law is studied. This is the simplest model of child's swing. Melnikov's analysis is carried out to find bifurcations of homoclinic,…
Louis Poinsot has shown in 1854 that the motion of a rigid body, with one of its points fixed, can be described as the rolling without slipping of one cone, the 'body cone', along another, the 'space cone', with their common vertex at the…
We study the geodesic motion of massless particles in singly rotating black ring spacetimes. We find stable stationary orbits of massless particles in toroidal spiral shape in the case that the thickness parameter of a black ring is less…
By folding an autonomous system of rational equations in the plane to a scalar difference equation, we show that the rational system has coexisting periodic orbits of all possible periods as well as stable aperiodic orbits for certain…
Putting several hard balls into a two-dimensional bowl can form a very basic two-dimensional model of hard-ball system. When the two-dimensional bowl has a parallel-rotation at a uniform speed around a center, when the number of balls is…
In this study, we formulate a set of differential equations for a binary system to describe the secular-tidal evolution of orbital elements, rotational dynamics, and deformation (flattening), under the assumption that one body remains…
Billiard systems offer a simple setting to study regular and chaotic dynamics. Gravitational billiards are generalizations of these classical billiards which are amenable to both analytical and experimental investigations. Most previous…
We study two notions. One is that of spindle convexity. A set of circumradius not greater than one is spindle convex if, for any pair of its points, it contains every short circular arc of radius at least one, connecting them. The other…
In this paper we consider cases of existence of invariant measure, additional first integrals, and Poisson structure in a problem of rigid body's rolling without sliding on plane and sphere. The problem of rigid body's motion on plane was…
The classical dynamics of the isotropic two-dimensional harmonic oscillator confined by an elliptic hard wall is discussed. The interplay between the harmonic potential with circular symmetry and the boundary with elliptical symmetry does…
In this article an analytical solution of equations of motion of a rigid disk of finite thickness rolling on its edge on a perfectly rough horizontal plane under the action of gravity is given. The solution is given in terms of Gauss…
The restricted three-vortex problem is investigated with one of the point vortices fixed in the plane. The motion of the free vortex having zero circulation is explored from a rotating frame of reference within which the free vortex with…
We prove the existence of some types of periodic orbits for a particle moving in Euclidean three-space under the influence of the gravitational force induced by a fixed homogeneous circle. These types include periodic orbits very far and…
We study polygonal billiards with one-sided vertical mirror scattered on a square billiard table. We associate trajectories of these kinds of billiards with double rotations and study orbit behavior and questions of complexity.
We discuss the interplay between the piece-line regular and vertex-angle singular boundary effects, related to integrability and chaotic features in rational polygonal billiards. The approach to controversial issue of regular and irregular…
The connected configuration space of a so called cylindric billiard system is a flat torus minus finitely many spherical cylinders. The dynamical system describes the uniform motion of a point particle in this configuration space with…