Two–Integral Models with Almost Circular Orbits

Exponents and Almost Periodic Orbits

We introduce the group of exponents of a map of the reals into a metric space and give conditions under which this group embeds in the first Čech cohomology group of the closure of the image of the map. We show that this group generalizes the subgroup of the reals generated by the Fourier-Bohr exponents of an almost periodic orbit and that any minimal almost periodic flow in a complete metric s...

Orbital phasing of satellites on circular orbits

Circular Orbits Inside the Sphere of Death

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.

Almost Periodic Orbits and Stability for Quantum Time-dependent Hamiltonians

We study almost periodic orbits of quantum systems and prove that for periodic time-dependent Hamiltonians an orbit is almost periodic if, and only if, it is precompact. In the case of quasiperiodic time-dependence we present an example of a precompact orbit that is not almost periodic. Finally we discuss some simple conditions assuring dynamical stability for nonautonomous quantum system.

Circular orbits in the extreme Reissner-Nordstrøm dihole metric

We study the motion of neutral test particles in the gravitational field of two charged black holes described by the extreme Reissner-Nordstrøm dihole metric where the masses and charges of the black holes are chosen such that the gravitational attraction is compensated by the electrostatic repulsion. We investigate circular orbits in the equatorial plane between the two black holes with equal ...