相关论文: Comment on "A Nonholonomic Model of the Paul Trap"

A rational theory is proposed to describe the large-scale motion in turbulence. The fluid element with inner orientational structures is proposed to be the building block of fluid dynamics. The variance of the orientational structures then…

The controlled motion of a rolling ball actuated by internal point masses that move along arbitrarily-shaped rails fixed within the ball is considered. Application of the variational Pontryagin's minimum principle yields the ball's…

The present paper derives the post-Newtonian Lagrangian of translational motion of N arbitrary-structured bodies with all mass and spin multipoles in a scalar-tensor theory of gravity. The multipoles depend on time and evolve in accordance…

The stability of the orbital motion of two long cylindrical magnets interacting exclusively with magnetic forces is described. To carry out analytical studies a model of magnetically interacting symmetric tops [1] is used. The model was…

The Looping pendulum phenomenon was first introduced in 2019 at the 32nd edition of the IYPT, wherein a lighter bob sweeps around a cylindrical rod to support the weight of a heavier bob. In this paper, the phenomenon was divided based on…

We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of regular and non-regular time-dependent mechanical systems, which is based on the approach of Skinner and Rusk (1983). The dynamical…

In this article, continuing the work done in the previous paper (M. Fathi 2012), we apply a Lagrangian formalism to demonstrate the shape of the geodesic motion for a massive charged particle which is falling freely in a de Sitter…

There are many different formulations of relativistic elasticity. Most of them are only concerned with formal questions rather than questions regarding the PDE point of view. The aim of this thesis is to obtain various local existence…

For a one-dimensional conservative systems with position depending mass, one deduces consistently a constant of motion, a Lagrangian, and a Hamiltonian for the non relativistic case. With these functions, one shows the trajectories on the…

We derive the dynamics of several rigid bodies of arbitrary shape in a 2-dimensional inviscid and incompressible fluid, whose vorticity field is given by point vortices. We adopt the idea of Vankerschaver et al. (2009) to derive the…

We present a detailed theoretical analysis of micro-motion in a time-averaged orbiting potential trap. Our treatment is based on the Gross-Pitaevskii equation, with the full time dependent behaviour of the trap systematically approximated…

We review the recent results on development of vector models of spin and apply them to study the influence of spin-field interaction on the trajectory and precession of a spinning particle in external gravitational and electromagnetic…

This paper studies various aspects of the motion of relativistic rotators, both in the presence and absence of external fields, using a toy model which, in a sense, can be regarded as a non-relativistic limit of the rotators. In a simpler…

We reexamine the problem of having nonconservative equations of motion arise from the use of a variational principle. In particular, a formalism is developed that allows the inclusion of fractional derivatives. This is done within the…

We study the relativistic formulation of a classical time-dependent nonholonomic Lagrangian mechanics from the perspective of moving frames. We also introduce time-dependent $G$-Chaplygin systems with affine constraints, which are natural…

Paul traps are ion traps that are widely used in spectroscopic experiments to confine and stabilize a charged particle within a small region using oscillating electric fields. The dynamics of the particle inside a Paul trap is described by…

In particle physics, most of the classical models consider that the centre of mass and centre of charge of an elementary particle, are the same point. This presumes some particular relationship between the charge and mass distribution, a…

Following the Poincare algebra for a free spinning particle and using the Casimirs of the algebra in the Hamiltonian approach, we construct systematically a set of Lagrangians for the relativistic spinning particle which includes the…

The need to develop models to predict the motion of microrobots, or robots of a much smaller scale, moving in fluids in a low Reynolds number regime, and in particular, in non Newtonian fluids, cannot be understated. The article develops a…

We study the dynamics of the center of mass of a Brownian particle levitated in a Paul trap. We focus on the overdamped regime in the context of levitodynamics, comparing theory with our numerical simulations and experimental data from a…