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We discuss some Lagrangian and presymplectic models concerning test particles in electromagnetic and gravitational fields, with the aim of describing an upper bound to the acceleration. Some models are based on the relativistic phase space…

Cosmic acceleration may be the result of unknown physical processes involving either new fields in high energy physics or modifications of gravitation theory. In the latter case, such modifications are usually related to the existence of…

The paper is based on the recently proposed 4-dimensional optical space theory and draws some of its consequences for gravitation. Starting with the discussion of central movement, the paper proceeds to establish the a metric compatible…

The aim of the present article is to give an exact and correct representation of the essentially important part of modern special relativity theory that touches upon the behavior of the proper length of accelerated moving bodies.In…

A classical and a relativistic law of motion for an advancing shell are deduced applying the thin layer approximation. A new parameter connected with the quantity of absorbed matter in the expansion is introduced; this allows of matching…

We investigate the effects of the aberration of light for a uniformly accelerating observer. The observer we consider is initially at rest with respect to a luminous spherical object--a star, say--and then starts to move away with constant…

We discuss and compare several geometric structures which imply an upper bound to the acceleration of a particle measured in its rest system. While all of them have the same implications on the motion of a point particle, they differ in…

Discrete mechanics is used to present fluid mechanics, fluid-structure interactions, electromagnetism and optical physics in a coherent theoretical and numerical approach. Acceleration considered as an absolute quantity is written as a sum…

A human creates an image basing on the information delivered by photons that arrived at his retina simultaneously. Due to finite and constant velocity of light these photons left the moving body at different times, since not all points of…

One possible explanation for the present observed acceleration of the Universe is the breakdown of homogeneity and isotropy due to the formation of non-linear structures. How inhomogeneities affect the averaged cosmological expansion rate…

This paper presents some novel contributions to the theory of inviscid flow regarding the forces exerted on a body moving through such a fluid in two dimensions. It is argued that acceleration of the body corresponds to vorticity generation…

We consider the evolution of a small rigid body in an incompressible viscous fluid filling the whole space $\rline^3$. When the small rigid body shrinks to a "massless" point in the sense that its density is constant, we prove that the…

We introduce and study the mechanical system which describes the dynamics and statics of rigid bodies of constant density floating in a calm incompressible fluid. Since much of the standard equilibrium theory, starting with Archimedes,…

We consider the motion of a particle on a surface which is a small perturbation of the standard sphere. One may qualitatively describe the motion by means of a precessing great circle of the sphere. The observation is employed to derive a…

Bubbles rising in viscoelastic liquids may exhibit a jump discontinuity of the rise velocity as a critical bubble volume is exceeded. The phenomenon has been extensively investigated in the literature, both by means of experiments as well…

The two-dimensional motion of an object on a moving rough horizontal plane is investigated. Two cases are studied: the plane having a translational acceleration, and a rotating plane. For the first case, the motions of a point particle and…

Superfluidity, the ability of a fluid to move without dissipation, is one of the most spectacular manifestations of the quantum nature of matter. We explore here the possibility of superfluid motion of light. Controlling the speed of a…

What does it mean to ``add'' velocities relativistically -- clarification of the conceptual problems, new derivations of the related formulas, and identification of the source of the non-associativity of the standard vector version of the…

The motion of a rotating helical body in a viscoelastic fluid is considered. In the case of force-free swimming, the introduction of viscoelasticity can either enhance or retard the swimming speed and locomotive efficiency, depending on the…

The problem of estimating the angular speed of a solid body from attitude measurements is addressed. To solve this problem, we propose an observer whose dynamics are not constrained to evolve on any specific manifold. This drastically…