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Newton's Theorem of Revolving Orbits derives the force that is necessary to explain a particular precession that leaves the shape of an orbit unchanged. Newton showed that for an orbiting body that is already subject to any central force,…
Dynamics of active deformable particles in an external Poiseuille flow is investigated. In order to make the analysis general, we employ time-evolution equations derived from symmetry considerations that take into account an elliptical…
It has been argued that an extended, quasi-rigid body evolving freely in curved spacetime can deviate from its natural trajectory by simply performing cyclic deformations. More interestingly, in the limit of rapid cycles, the amount of…
We analyze the frictionless motion of a point-like particle that slides under gravity on an inverted conical surface. This motion is studied for arbitrary initial conditions and a general relation, valid within 13%, between the periods of…
Due to Poinsot's theorem, the motion of a rigid body about a fixed point is represented as rolling without slipping of the moving hodograph of the angular velocity over the fixed one. If the moving hodograph is a closed curve, visualization…
In this paper we study the controlled motion of an arbitrary two-dimensional body in an ideal fluid with a moving internal mass and an internal rotor in the presence of constant circulation around the body. We show that by changing the…
Energy is in general not conserved for mechanical nonholonomic systems with affine constraints. In this article we point out that, nevertheless, in certain cases, there is a modification of the energy that is conserved. Such a function…
A family of angular momentum coherent states on the sphere is constructed using previous work by Aragone et al [1]. These states depend on a complex parameter which allows an arbitrary squeezing of the angular momentum uncertainties. The…
The influence of the size and shape of a dispersing and absorbing dielectric body on the local-field corrected spontaneous-decay of an excited atom embedded in the body is studied on the basis of the real-cavity model. By means of a Born…
A three-dimensional deformable capsule convected through a square duct with a corner is studied via numerical simulations. We develop an accelerated boundary integral implementation adapted to general geometries and boundary conditions. A…
In this paper, we study the bulk motion of a classical extended charge in flat spacetime. A formalism developed by W. G. Dixon is used to determine how the details of such a particle's internal structure influence its equations of motion.…
Although the gravity dependence of granular friction is crucial to understand various natural phenomena, its precise characterization is difficult. We propose a method to characterize granular friction under various gravity (body force)…
Physical geometry studies mutual disposition of geometrical objects and points in space, or space-time, which is described by the distance function d, or by the world function \sigma =d^{2}/2. One suggests a new general method of the…
We consider the motion of a two-dimensional body of arbitrary shape in a planar irrotational, incompressible fluid with a given amount of circulation around the body. We derive the equations of motion for this system by performing…
Three-dimensional central symmetric bodies different from spheres that can float in all orientations are considered. For relative density rho=1/2 there are solutions, if holes in the body are allowed. For rho different from 1/2 the body is…
Composite system made of $N$ particles is considered in twist-deformed space-time. It is shown that in the space the motion of the center-of-mass of the system depends on the relative motion. Influence of deformation on the motion of the…
Based on Bohr model, we have presented a general formalism describing the collective motion for any deformed system, in which the collective Hamiltonian is expressed as vibrations in the body-fixed frame, rotation of whole system around the…
A theory of self-propelled particles is developed in two dimensions assuming that the particles can be deformed from a circular shape when the propagating velocity is increased. A coupled set of equations in terms of the velocity and a…
We study influence of noncommutativity of coordinates and noncommutativity of momenta on the motion of a particle (macroscopic body) in uniform and non-uniform gravitational fields in noncommutative phase space of canonical type with…
Affine deformations serve as basic examples in the continuum mechanics of deformable 3-dimensional bodies (referred as homogeneous deformations). They preserve parallelism and are often used as an approximation to general deformations.…