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This work answers positively the question whether non-stop flights are possible for maintaining constant the pose of cable-suspended objects. Such a counterintuitive answer paves the way for a paradigm shift where energetically efficient…
The problem of a disc and a ball rolling on a horizontal plane without slipping is considered. Differential constrained equations are shown to be integrated when the trajectory of the point of contact is taken in a form of the natural…
The article discusses the steady motion of a rigid disk of finite thickness rolling on its edge on a horizontal plane under the influence of gravity. The governing equations are presented and two cases allowing for a steady state solution…
A wheel or sphere rolling without slipping on the inside of a sphere in a uniform gravitational field can have stable circular orbits that lie wholly above the "equator", while a particle sliding freely cannot.
The anomalous energy difference observed during the Earth flybys is modelled here as a dynamical effect resulting from the coupling of the gravitational and the magnetic fields of the Earth. The theoretical analysis shows that general…
Suppose curves are moving by curvature in a plane, but one embeds the plane in $R^3$ and looks at the plane from an angle. Then circles shrinking to a round point would appear to be ellipses shrinking to an ``elliptical point,'' and the…
The assumption of asymptotic flatness for isolated astrophysical bodies may be considered an approximation when one considers a cosmological context where a cosmological constant or vacuum energy is present. In this framework we study the…
We consider the vibrations and waves in the atmosphere under the gravitation on the flat earth. The stratified density distribution of the back ground equilibrium is supposed to touch the vacuum at the finite height of the stratosphere. We…
The flyby anomalies are unexplained velocity jumps of 3.9, -4.6, 13.5, -2, 1.8 and 0.02 mm/s observed near closest approach during the Earth flybys of six spacecraft. These flybys are modelled here using a theory that assumes that inertia…
One of two postulates that are base for special relativity is that the laws of physics are invariant in all inertial systems, which has as a consequence that it is impossible for an observer to detect his motion through space. It will be…
We study the geometric effects of our galaxy's peculiar motion on the circles-in-the-sky. We show that the shape of these circles-in-the-sky remains circular, as detected by a local observer with arbitrary peculiar velocity. Explicit…
We consider the oscillations of the atmosphere around a stratified back ground density and entropy distribution under the gravitation on the flat Earth. The atmosphere is supposed to be an ideal gas and the motion is supposed to be governed…
We consider the problem of mirror invisibility for plane sets. Given a circle and a finite number of unit vectors (defining the directions of invisibility) such that the angles between them are commensurable with $\pi$, for any $\varepsilon…
Light's orbital angular momentum (OAM) is a conserved quantity in cylindrically symmetric media; however, it is easily destroyed by free-space turbulence or fiber bends, because anisotropic perturbations impart angular momentum. We observe…
Study of the classical motion of two identical particles on a plane subject to non-Coulomb potentials in a constant magnetic field presented in polar coordinates. With the rigorous analysis of the potentials and the constants of motion, we…
A family of plane oriented continuous paths depending on a fixed real positive number $R$ is considered. For any point $x$ on the path, the previous points lie out of any circle of radius $R$ having at $x$ interior normal in a suitable…
The trajectory of a spherical object which falls freely in a gravitational field is fixed by its initial position and velocity. However, an object which can control its shape can also control its motion: Except where forbidden by symmetries…
The cohesive collective motion (flocking, swarming) of autonomous agents is ubiquitously observed and exploited in both natural and man-made settings, thus, minimal models for its description are essential. In a model with continuous space…
The general circulation of the atmosphere determines the long-term variability of weather processes. This circulation is driven by the temperature differences between the poles and the equator, causing air to move along the Earth's surface.…
We study the motion of a charged particle under the action of a magnetic field with cylindrical symmetry. In particular we consider magnetic fields with constant direction and with magnitude depending on the distance $r$ from the symmetry…