Related papers: Using the Euler method in a spreadsheet to study a…
We consider the Euler system describing a one-dimensional inviscid flows in space along curves of a certain class. Using differential invariants for the Euler system, we obtain its quotient equation. The solutions of the quotient equation…
Solar arrays are structures which are connected to satellites; during launch, they are in a folded position and submitted to high vibrations. In order to save mass, the flexibility of the panels is not negligible and they may strike each…
The spectrum of oscillating compact objects can be considerably altered in alternative theories of gravity. In particular, it may be enriched by modes with no counterpart in general relativity, tied to the dynamics of additional degrees of…
This paper is devoted to the study of periodic solutions for a semilinear Euler-Bernoulli beam equation with variable coefficients. Such mathematical model may be described the infinitesimal, free, undamped in-plane bending vibrations of a…
The dynamics for a thin, closed loop inextensible Euler's elastica moving in three dimensions are considered. The equations of motion for the elastica include a wave equation involving fourth order spatial derivatives and a second order…
We investigate the nonlinear effect of a pendulum with the upper end fixed to an elastic rod which is only allowed to vibrate horizontally. The pendulum will start rotating and trace a delicate stationary pattern when released without…
We have designed an experiment that involves studying the effects of a conducting plate on the motion of an oscillating disc magnet. We have employed the video analysis method by Tracker software to investigate the variation of…
The development of efficient and robust dynamic models is fundamental in the field of systems and control engineering. In this paper, a new formulation for the dynamic model of nonlinear mechanical systems, that can be applied to different…
The search for Noether point symmetries for non-relativistic charged particle motion is reduced to the solution for a set of two coupled, linear partial differential equations for the electromagnetic field. These equations are completely…
We propose a discussion of angular momentum and its Euler equation, with the aim of giving a short outline of their history. This outline can be useful for teaching purposes too, to amend some problems that students can have in learning…
Intrinsic thermal fluctuations within a real solid challenge the rigid body assumption that is central to Euler's equations for the motion of a free body. Recently, we have introduced a dissipative and stochastic version of Euler's…
The dynamics along the particle trajectories for the 3D axisymmetric Euler equations in an infinite cylinder are considered. It is shown that if the inflow-outflow is highly oscillating in time, the corresponding Euler flow cannot keep the…
The classical and quantum oscillator model on Lie-algebraically deformed nonrelativistic space-time is introduced and analyzed. The corresponding equations of motions are studied using mostly numerical methods. The time-dependent energy…
We design a low-cost, electromagnetically coupled, simple harmonic oscillator and demonstrate free, damped and forced oscillations in an under-graduate (UG) Physics laboratory. It consists of a spring-magnet system that can oscillate inside…
A continuum evolutionary model for micromagnetics is presented that, beside the standard magnetic balance laws, includes thermo-magnetic coupling. To allow conceptually efficient computer implementation, inspired by relaxation method of…
We compute electromagnetic wave propagation through the magnetosphere of a magnetar. The magnetosphere is modeled as the QED vacuum and a cold, strongly magnetized plasma. The background field and electromagnetic waves are treated…
In this letter we study the classical motion of an electric dipole in the presence of a uniform magnetic field in the approximation of small oscillations. The normal modes of oscillations are obtained and propose a criterion of…
A generalization of the Euler's elastic problem, i.e., finding a stationary configuration (planar elastica) of the Bernoulli's thin ideal elastic rod with boundary conditions defined through fixed endpoints and/or tangents at the endpoints,…
A linear theory of whistler wave is developed wihtin the paradigm of a two dimensional incompressible electron magnetohydrodynamics model. Exact analytic wave solutions are obtained for a small amplitude whistler wave that exhibit magnetic…
This paper presents a novel type of mobile rolling robot designed as a modular platform for non-prehensile manipulation, highlighting the associated control challenges in achieving balancing control of the robotic system. The developed…