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An approximate solution is presented for simple harmonic motion in the presence of damping by a force which is a general power-law function of the velocity. The approximation is shown to be quite robust, allowing for a simple way to…
We show asymptotic, exponential stability of the equilibrium configuration, $\smallL$, of a hollow physical pendulum with its inner part entirely filled with a viscous liquid, corresponding to the center of mass being in the lowest…
We provide analytic solutions of the nonlinear differential equation system describing the particle paths below small-amplitude periodic gravity waves travelling on a constant vorticity current. We show that these paths are not closed…
We are concerned with the existence and boundary behaviour of positive radial solutions for the system \begin{equation*} \left\{ \begin{aligned} \Delta u&=g(|x|,v(x)) &&\quad\mbox{in}\ \Omega, \\ \Delta v&=f(|x|,|\nabla u(x)|)…
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…
The motion of a particle with a spin in spherical harmonic oscillator potential with spin-orbit interaction is studied. We have focus our attention on spatial motion of wave packets, giving a description complementary to motion of spin…
In the present paper, we study a new type of large-scale instability, which arises in obliquely rotating electroconductive fluids with a small-scale external force of zero helicity. This force excites small-scale velocity oscillations with…
We consider classical dynamical properties of a particle in a constant gravitational force and making specular reflections with circular, elliptic or oval boundaries. The model and collision map are described and a detailed study of the…
This paper presents a variational approach to doubly-nonlinear (gradient) flows (P) of nonconvex energies along with nonpotential perturbations (i.e., perturbation terms without any potential structures). An elliptic-in-time regularization…
We investigate the problem of determining the shape of a rotating celestial object - e.g., a comet or an asteroid - under its own gravitational field. More specifically, we consider an object symmetric with respect to one axis - such as a…
We find a solution of a quasilinear elliptic equation with Dirichlet's boundary condition on a smooth bounded domain and involving an unbounded continuous nonlinearity with oscillatory behavior near the origin.
Positive solutions of homogeneous Dirichlet boundary value problems or initial-value problems for certain elliptic or parabolic equations must be radially symmetric and monotone in the radial direction if just one of their level surfaces is…
The wide applications of higher dimensional gravity and gauge/gravity duality have fuelled the search for new stationary solutions of the Einstein equation (possibly coupled to matter). In this topical review, we explain the mathematical…
In this paper we study the global dynamics of the inverted spherical pendulum with a vertically vibrating suspension point in the presence of an external horizontal periodic force field. We do not assume that this force field is weak or…
Vortices (flows with closed elliptic streamlines) are exact nonlinear solutions to the compressible Euler equation. In this contribution, we use differential geometry to derive the transformations between Cartesian and elliptic coordinates,…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider orbital motion in transverse plane for a single…
We study the fluctuation-electromagnetic interaction between a small rotating particle with an arbitrary direction of angular velocity vector and evanescent field of the heated surface, and obtain the general expressions for the force of…
The study of the motion of a rigid body on a plane (RBP motion) is usually one of the most challenging topics that students face in introductory physics courses. In this paper, we discuss a couple of problems which are typically used in…
We present a novel numerical method to calculate periodic orbits for dynamical systems by an iterative process which is based directly on the action integral in classical mechanics. New solutions are obtained for the planar motion of three…
The problem of a disc and a ball rolling on a horizontal plane without slipping is considered. Differential constrained equations are shown to be integrated when the trajectory of the point of contact is taken in a form of the natural…