Related papers: New Equation for Bending Development of Arbitrary …
A new equation is proposed to explain the curvature of spent sparklers. We found the state of a segment of the sparkler to depend strongly on the state of its spent segments. The equation is nearly able to produce the sparkler shape for a…
Considered typical processes of rod bending under strong longitudinal compression. The dynamic equation of bending correspponds to a perturbation of the two- dimensional Laplace equation. It is established that, for these processes,…
Using continuation methods, we study the global solution structure of periodic solutions for a class of periodically forced equations, generalizing the case of relativistic pendulum. We obtain results on the existence and multiplicity of…
We demonstrate how one can describe explicitly the present arbitrariness in solutions of relativistic wave equations in external electromagnetic fields of special form. This arbitrariness is connected to the existence of a transformation,…
We present a unified classical treatment of partially constrained elastic rods. Partial constraints often entail singularities in both shapes and reactions. Our approach encompasses both sleeve and adhesion problems, and provides simple and…
We examine the reductions of the order of certain third- and second-order nonlinear equations with arbitrary nonlinearity through their symmetries and some appropriate transformations. We use the folding transformation which enables one to…
Problems involving rotating systems analyzed from an inertial frame, without invoking fictitious forces, is something that freshman students find difficult to understand in an introductory mechanics course. One of the problems that I…
We discuss the equation of motion of the driven pendulum and generalize it to arbitrary driving angle. The pendulum will oscillate about a stable angle other than straight down if the drive amplitude and frequency are large enough for a…
In this paper, we consider rods whose thickness vary linearly between $\eps$ and $\eps^2$. Our aim is to study the asymptotic behavior of these rods in the framework of the linear elasticity. We use a decomposition method of the…
Linearised relativistic elasticity equations of motion are considered for a rod and a spinning ring encountering a gravitational wave. In the case of the rod, the equations reduce to a wave equation with appropriate boundary conditions.…
We consider the dynamical evolution of a thin rod described by an appropriately scaled wave equation of nonlinear elasticity. Under the assumption of well-prepared initial data and external forces, we prove that a solution exists for…
A simple Lagrangian is proposed that by the choice of the representation of SU(2), gives rise to field equations for arbitrary spin. In explicit examples it is shown, how the Klein-Gordon, the Dirac, and the Proca equation can be obtained…
We study three-dimensional deformations of thin inextensible elastic rods with non-vanishing spontaneous curvature and torsion. In addition to the usual description in terms of curvature and torsion which considers only the configuration of…
The relativistic motion of an arbitrary point of an accelerated rigid rod is discussed for the case when velocity and acceleration are directed along the rod's length. The discussion includes the case of a time-dependent force applied to a…
We consider the forced motion of a relativistic particle constrained on a curve and present sufficient conditions for periodic oscillations by means of an illustrative geometrical approach. Obtained result is illustrated by a few examples…
A new apparent relativistic paradox is presented involving only one space-time event. This is different from earlier relativistic paradoxes involving extended bodies or events at different positions. A collision between a rod and a ring…
In the special relativity, a rigid rod slides upon itself, with one extremity oscillating harmonically. We discovered restrictions in the amplitude of the motion and in the length of the rod, essential to eliminate unphysical solutions.…
We present a new exact solution for the twist of an asymmetric thin elastic rods. The shape of such rods is described by the static Kirchhoff equations. In the case of constant curvatire and torsion the twist of the asymmetric rod…
Using the damped pendulum system we introduce the averaging method to study the periodic solutions of a dynamical system with small perturbation. We provide sufficient conditions for the existence of periodic solutions with small amplitude…
The method of this paper is my original creation. A new method for solving linear differential equations is proposed in this paper. The important conclusion of this paper is that arbitrary order linear ordinary differential equations with…