经典物理

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…

The problem of constant-speed ballistics is studied under the umbrella of non-linear non-holonomic constrained systems. The Newtonian approach is shown to be equivalent to the use of Chetaev's rule to incorporate the constraint within the…

We solve a set of selected exercises on rotational motion requiring a mechanical and thermodynamical analysis. When non-conservative forces or thermal effects are present, a complete study must use the first law of thermodynamics together…

Optimal impedance for each mode is an important concept in an infinitely long duct lined with uniform absorption material. However it is not valid for finite length linings. This is because that the modes in lined ducts are not…

We show that for isolated relativistic systems with spin the conservation of total angular momentum implies that, instead of the center of mass, it is a modified center of mass and spin which behaves inertially. This requires a change in…

When explaining to a lay audience the magnitude of forces or accelerations imparted to vehicles or experienced by vehicle occupants during a motor vehicle collision, it is often helpful to recast the critical results in terms of other…

The paper includes two contributions. First, it proves that the series and shunt radiation components, corresponding to longitudinal and transversal electric fields, respectively, are always in phase quadrature in axially asymmetric…

Suppose that $H(q,p)$ is a Hamiltonian on a manifold $M$, and $\tilde L(q,\dot q)$, the Rayleigh dissipation function, satisfies the same hypotheses as a Lagrangian on the manifold $M$. We provide a Hamiltonian framework that gives the…

Non-local elasticity models in continuum mechanics can be treated with two different approaches: the gradient elasticity models (weak non-locality) and the integral non-local models (strong non-locality). This article focuses on the…

In this article, we present a set of rigorous derivations of the equations used in planar impact dynamics calculations, in the context of vehicular accident reconstruction.

Since they correspond to a jump from a given note to another one, the mouth pressure thresholds leading to regime changes are particularly important quantities in flute-like instruments. In this paper, a comparison of such thresholds…

It is shown that given an arbitrary canonical transformation and an arbitrary Hamiltonian, there is a naturally defined mapping that sends any solution of the Hamilton-Jacobi (HJ) equation into a solution of the HJ equation corresponding to…

We derive the radiation reaction by taking into account that the acceleration of the charge is caused by the interaction with some heavy source particle. In the non relativistic case this leads, in contrast to the usual approach,…

We analyze, from the thermodynamical point of view, mechanical systems in which there is production of mechanical energy due to an internal source of energy, and compare that analysis with the similar one for the "symmetric" motion which…

The behavior of a distributed charge in a Coulomb potential well is considered. It is shown that elements of a distributed charge can move along different trajectories, thus forming actually motion of a charge wave. Propagation over…

Acoustic cloaks that make object undetectable to sound waves have potential applications in a variety of scenarios and have received increasing interests recently. However, the experimental realization of a three-dimensional (3D) acoustic…

The universal mechanism of trapping and localization of sufficiently slow-speed particles by a potential well deepening with time is established on the basis of fundamental relations of classical mechanics. Such wells may be created for a…

A significantly lower upper limit to minimum energy solutions of the electrostatic Thomson Problem is reported. A point charge is introduced to the origin of each $N$-charge solution. This raises the total energy by $N$ as an upper limit to…

Correspondences between the Thomson Problem and atomic electron shell-filling patterns are observed as systematic non-uniformities in the distribution of potential energy necessary to change configurations of $N\le 100$ electrons into…

Recently, the spinning tethered system is regarded as a typical and fundamental space structure attracting great interest of the aerospace engineers, and has been discussed primarily for specific space missions in past decades, including…