相关论文: Circular orbits of a ball on a rotating conical tu…

This paper addresses the problem of the Chaplygin ball rolling on a horizontal plane which rotates with constant angular velocity. In this case, the equations of motion admit area integrals, an integral of squared angular momentum and the…

It is often assumed that a warped galaxy can be modeled by a set of rings. This paper verifies numerically the validity of this assumption by the study of periodic orbits populating a heavy self-gravitating warped disk. The phase space…

A series of experiments for steady state rotation of water in vessels of various geometries is presented. The experiments focus on the geometrical characteristics of the rotating liquids and the change in their surface topology, from that…

The motion of two pairs of counter-rotating point vortices placed in a uniform flow past a circular cylinder is studied analytically and numerically. When the dynamics is restricted to the symmetric subspace---a case that can be realized…

Spiral waves in active media react to small perturbations as particle-like objects. Here we apply the asymptotic theory to the interaction of spiral waves with a localized inhomogeneity, which leads to a novel prediction: drift of the…

We study the rolling motion of a small solid sphere on a surface patterned rubber substrate in an external field with and without a noise. In the absence of the noise, the ball does not move below a threshold force above which it…

We study the classical and quantum mechanics of a three-dimensional stadium billiard. It consists of two quarter cylinders that are rotated with respect to each other by 90 degrees, and it is classically chaotic. The billiard exhibits only…

In the paper discusses the interaction between two charged balls in equilibrium state. It is shown that, depending of the sizes, charges and distance, the balls can move in the same or opposite direction. They can repulse and attract. It is…

Mathematical billiards is much like the real game: a point mass, representing the ball, rolls in a straight line on a (perfectly friction-less) table, striking the sides according to the law of reflection. A billiard trajectory is then…

A detailed study of the classical and quantum mechanics of a free particle on a double cone and the particle bounded to its tip by the harmonic oscillator potential is presented.

We investigate a rotated, orthogonal gravitational wedge billiard - a special case of the asymmetric wedge billiard - in which the dynamics are integrable. We derive equations and conditions under which periodic orbits may be constructed…

We explore the complex dynamics of a non-coalescing drop of moderate size inside a circular hydraulic jump of the same liquid formed on a horizontal disk. In this situation the drop is moving along the jump and one observes two different…

We consider the problem of a sphere rolling of a curved surface and solve it by mapping it to the precession of a spin 1/2 in a magnetic field of variable magnitude and direction. The mapping can be of pedagogical use in discussing both…

The stability of rotating isotropic spherical stellar systems is investigated by using N-body simulations. Four spherical models with realistic density profiles are studied: one of them fits the luminosity profile of globular clusters,…

The two-dimensional motion of an object on a moving rough horizontal plane is investigated. Two cases are studied: the plane having a translational acceleration, and a rotating plane. For the first case, the motions of a point particle and…

The dynamics of a rigid, rotating, precessing, massive ring orbiting a point mass within the perimeter of the ring are considered. It is demonstrated that orbits dynamically stable against perturbations in three dimensions exist for a range…

Billiard systems, broadly speaking, may be regarded as models of mechanical systems in which rigid parts interact through elastic impulsive (collision) forces. When it is desired or necessary to account for linear/angular momentum exchange…

Nonholonomic systems are variational models commonly used for mechanical systems with ideal no-slip constraints. This note provides a differential-geometric derivation of the nonholonomic equations of motion for an arbitrary rigid body…

In this paper we define and study the billiard problem on bounded regions on surfaces of constant curvature. We show that this problem defines a 2-dimensional conservative and reversible dynamical system, defined by a Twist diffeomorphism,…

We consider the vertical motion of a free falling ball bouncing elastically on a racket moving in the vertical direction according to a regular $1$-periodic function $f$. For fixed coprime $p,q$ we study existence, stability in the sense of…