Related papers: The motion of a leaking oscillator -- a study for …

The problem of the existence and uniqueness of the motion of the system of an arbitrary number linear oscillators under a generalized dry-friction type control is studied. This type of control arises in the problem of steering the system to…

The following offers a new axiomatic basis of mechanics and physics in their most important dynamics domain, i. e. an axiom (principle) of completeness intended to generalize Newton's second law of motion for the case of a non-stationary…

Over the past decade the study of fluidic droplets bouncing and skipping (or ``walking'') on a vibrating fluid bath has gone from an interesting experiment to a vibrant research field. The field exhibits challenging fluids problems,…

The harmonic oscillator plays a central role in physics describing the dynamics of a wide range of systems close to stable equilibrium points. The nonrelativistic one-dimensional spring-mass system is considered a prototype representative…

We study the effects of the electromagnetic vacuum on the motion of a nonrelativistic electron. First, we derive the equation of motion for the expectation value of the electron's position operator. We show how this equation has the same…

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…

We discuss several approaches to generalized solutions of problems describing the motion of inviscid fluids. We propose a new concept of dissipative solution to the compressible Euler system based on a careful analysis of possible…

The study of creeping motion of viscoelastic fluid around a rotating rigid torus is investigated. The analysis of the problem is performed using a second-order viscoelastic model. The study is carried out in terms of the bipolar toroidal…

We investigate quantum effects in the evolution of general systems. For studying such temporal quantum phenomena, it is paramount to have a rigorous concept and profound understanding of the classical dynamics in such a system in the first…

For a one-dimensional motion, a constant of motion for non autonomous an linear system (position and velocity) is given from the constant of motion associated to its autonomous system. This approach is used in the study of the harmonic…

A mathematical model is derived for the dynamics of a cylinder, or wheel, rolling over a thin viscous film. The model combines the Reynolds lubrication equation for the fluid with an equation of motion for the wheel. Two asymptotic limits…

The diffusion in two dimensions of non-interacting active particles that follow an arbitrary motility pattern is considered for analysis. Accordingly, the transport equation is generalized to take into account an arbitrary distribution of…

A mathematical model describing the erosion or leaching of a solid material by a flowing fluid in a column is developed. This involves an advection-diffusion equation coupled to a linear kinetic reaction describing the mass transfer between…

We give a partial answer to the question whether the Schrodinger equation can be derived from the Newtonian mechanics of a particle in a potential subject to a random force. We show that the fluctuations around the classical motion of a one…

An internal energy function of the mass density, the volumetric entropy and their gradients at n-order generates the representation of multi-gradient fluids. Thanks to Hamilton's principle, we obtain a thermodynamical form of the equation…

The motion of a deformable active particle in linear shear flow is explored theoretically. Based on symmetry considerations, in two spatial dimensions, we propose coupled nonlinear dynamical equations for the particle position, velocity,…

In this paper a rotating two-fluid model for the propagation of internal waves is introduced. The model can be derived from a rotating-fluid problem by including gravity effects or from a nonrotating one by adding rotational forces in the…

Within the so-called scaled quantum theory, the standard bouncing ball problem is analyzed under the presence of a gravitational field and harmonic potential. In this framework, the quantum-classical transition of the density matrix is…

We explore the relationship between mechanical systems describing the motion of a particle with the mechanical systems describing a continuous medium. More specifically, we will study how the so-called intermediate integrals or fields of…

Newton's laws of motion pose an apparent problem, sometimes referred to as "the independence problem": the first law seems to be a simple consequence of the second law, raising the question of why it was included as a separate law. Numerous…