Related papers: Hyperbolic motion generated by inversion
A recent paper [CGT] studies the evolution of star-shaped mean convex hypersurfaces of the Euclidean space by a class of nonhomogeneous expanding curvature flows. In the present paper we consider the same problem in the real, complex and…
It is shown that abelian Higgs vortices on a hyperbolic surface $M$ can be constructed geometrically from holomorphic maps $f:M \to N$, where $N$ is also a hyperbolic surface. The fields depend on $f$ and on the metrics of $M$ and $N$. The…
It is shown that the action for Hamiltonian equations of motion can be brought into invariant symplectic form. In other words, it can be formulated directly in terms of the symplectic structure $\omega$ without any need to choose some…
We present a topological proof of the existence of a normally hyperbolic invariant manifold for maps. In our approach we do not require that the map is a perturbation of some other map for which we already have an invariant manifold. But a…
The kinetic Brownian motion on the sphere bundle of a Riemannian manifold $M$ is a stochastic process that models a random perturbation of the geodesic flow. If $M$ is a orientable compact constant negatively curved surface, we show that in…
We provide a general algorithm to construct a Hamiltonian, such that its dynamical flow covariantly defines any given spherically symmetric and static metric. This Hamiltonian is defined as a linear combination of the standard (general…
The uniformly accelerated reference frame described by Hamilton, Desloge and Philpott involves the observers who perform the hyperbolic motion with constant proper acceleration gi. They start to move from different distances measured from…
Equation of motion and the vector of perturbing acceleration (force) for the galactic tide in a noninertial frame of reference is derived. The noninertial reference frame is rotating with a fixed angular velocity $\vec{\omega}$ $=$ $-$…
We establish H\"older stability of an inverse hyperbolic obstacle problem. Mainly, we study the problem of reconstructing an unknown function defined on the boundary of the obstacle from two measurements taken on the boundary of a domain…
Timelike geodesics on a hyperplane orthogonal to the symmetry axis of the G\"odel spacetime appear to be elliptic-like if standard coordinates naturally adapted to the cylindrical symmetry are used. The orbit can then be suitably described…
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…
The shortening of bodies in the direction of motion, Lorentz contraction, follows from the solution of Maxwell's equations. Moving light clocks will tick slower than those at rest because the speed of light does not depend on a source of…
An inverse cascade - energy transfer to progressively larger scales - is a salient feature of two-dimensional turbulence. If the cascade reaches the system scale, it creates a coherent flow expected to have the largest available scale and…
Based on the Generalized Principle of Inertia, which states that: \emph{An inanimate object moves freely, that is, with zero acceleration, in its own spacetime, whose geometry is determined by all of the forces affecting it,} we geometrize…
We exhibit orbits of the geodesic flow on a hyperbolic surface with at least one cusp such that every tubular neighborhood contains uncountably many distinct geodesic flow orbits. The proof relies on new phenomena, namely the existence of…
The main purpose of this paper is to seek a mechanical interpretation of gravitational phenomena. We suppose that the universe may be filled with a kind of fluid which may be called the $\Omega (0)$ substratum. Thus, the inverse-square law…
The general construction of extended refrence frames for noninertial observers in flat space is studied. It is shown that, if the observer moves inertially before and after an arbitrary acceleration and rotation, the region where reference…
We investigate how a symmetric penetrable object immersed in an active fluid becomes motile due to a negative drag acting in the direction of its velocity. While similar phenomena have been reported only for active fluids that posses polar…
We construct a self-consistent relativistic Newtonian analogue corresponding to gravitational static spherical symmetric spacetime geometries, staring directly from a generalized scalar relativistic gravitational action in Newtonian…
The kinematics of a robot manipulator are described in terms of the mapping connecting its joint space and the 6-dimensional Euclidean group of motions $SE(3)$. The associated Jacobian matrices map into its Lie algebra $\mathfrak{se}(3)$,…