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A pseudo-Newtonian Hill problem based on the Paczynski-Wiita pseudo-Newtonian potential that reproduces general relativistic effects is presented and compared with the usual Newtonian Hill problem. Poincare maps, Lyapunov exponents and…
The Newtonian as well as the special relativistic dynamics are used to study the stability of orbits of a test particle moving around a black hole plus a dipolar halo. The black hole is modeled by either the usual monopole potential or the…
We study the effects of general relativistic gravity on the Hill stability, that is, the stability of a multi-body system against a close approach of one orbit to another, which has been hitherto studied mainly in Newtonian mechanics and…
The motion of a satellite around a planet can be studied by the Hill model, which is a modification of the restricted three body problem pertaining to motion of a satellite around a planet. Although the dynamics of the circular Hill model…
On the bases of the Papapetrou equations with various supplementary conditions and other approaches a comparative analysis of the equations of motion of rotating bodies in general relativity is made. The motion of a body with vertical spin…
We determine the general form of the potential of the problem of motion of a rigid body about a fixed point, which allows the angular velocity to remain permanently in a principal plane of inertia of the body. Explicit solution of the…
Orbit-attitude hovering of a spacecraft at the natural relative equilibria in the body-fixed frame of a uniformly rotating asteroid is discussed in the framework of the full spacecraft dynamics, in which the spacecraft is modeled as a rigid…
In this article we study the stability in the sense of Lyapunov of the circular orbits in the generalized Manev two bodies problem. First, we explore the existence of the circular orbits and determine their radius. Then, using the first…
Modified Newtonian potentials have been proposed for the description of relativistic effects acting on particles and fluids in permanent orbital motion around black holes. Here we further discuss spherically symmetric potentials like the…
In this article we consider the motion of two bodies under the action of a Manev central force. We obtain the radius of the circular orbit and analyze its stability in sense of Lyapunov. Drawn on the first integrals of angular momentum and…
We review the orbital stability of the planar circular restricted three-body problem, in the case of massless particles initially located between both massive bodies. We present new estimates of the resonance overlap criterion and the Hill…
The exact solution to the Einstein equations that represents a static axially symmetric source deformed by an internal quadrupole is considered. By using the Poincare section method we numerically study the geodesic motion of test…
A covariant hamiltonian formalism for the dynamics of compact spinning bodies in curved space-time in the test-particle limit is described. The construction allows a large class of hamiltonians accounting for specific properties and…
We consider the equatorial circular motion of a test particle of specific charge q/m << 1 in the Kerr-Newman geometry of a rotating charged black hole. We find the particle's conserved energy and conserved projection of the angular momentum…
We consider the problem of orbital stability of the motion of a test particle in the restricted three-body problem, by using the orbital moment and its time derivative. We show that it is possible to get some insight into the stability…
We study the dynamics of a rigid body in a central gravitational field modeled as a Hamiltonian system with continuous rotational symmetries following the geometrical framework of Wang et al. Novelties of our work are the use the Reduced…
We investigate the collective behaviour of particle orbits in the vicinity of magnetic reconnection in Earth's magneto-tail. Various regions of different kinds of orbital stability of particle motions are found. We locate regimes of…
We present a general framework for calculating post-Minskowskian, classical, conservative Hamiltonians for $N$ non-spinning bodies in general relativity from relativistic scattering amplitudes. Novel features for $N>2$ are described…
Continuing work initiated in an earlier publication [Yamada, Tsuchiya, and Asada, Phys. Rev. D 91, 124016 (2015)], we reexamine the linear stability of the triangular solution in the relativistic three-body problem for general masses by the…
We study the dynamics of the planar circular restricted three-body problem in the context of a pseudo-Newtonian approximation. By using the Fodor-Hoenselaers-Perj\'es procedure, we perform an expansion in the mass potential of a static…