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The aim of this note is to survey the results in some geometric problems related to the centroids and the static equilibrium points of convex bodies. In particular, we collect results related to Gr\"unbaum's inequality and the…
We consider the general spatial three body problem and study the dynamics of planetary systems consisting of a star and two planets which evolve into 2/1 mean motion resonance and into inclined orbits. Our study is focused on the periodic…
In this paper we study the linear stability of relative equilibria in the Newtonian $n$-body problem from the viewpoint of electromagnetic systems. We first examine the effect of the ambient dimension on stability, starting from the…
We consider the motion of point masses given by a natural extension of Newtonian gravitation to spaces of constant positive curvature. Our goal is to explore the spectral stability of tetrahedral orbits of the corresponding 4-body problem…
It is a classical result of Euler that the rotation of a torque-free three-dimensional rigid body about the short or the long axis is stable, whereas the rotation about the middle axis is unstable. This result is generalized to the case of…
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…
In this paper we consider the stabilization of non-fundamental unstable stationary solutions of the cubic nonlinear Schrodinger equation. Specifically we study the stabilization of radially symmetric solutions with nodes and asymmetric…
The Poynting-Robertson(P-R) effect on Lyapunov stability of equilibrium points is being discussed in the the generalized photogravitational Chermnykh's problem when bigger primary is a sours of radiation and smaller primary is an oblate…
We analyze in this paper the existence of the "out-of-plane" equilibrium points in the restricted three-body problem with oblateness. From the series expansion of the potential function of an oblate asteroid, we show analytically all…
Central configurations play an important role in the dynamics of the $n$-body problem: they occur as relative equilibria and as asymptotic configurations in colliding trajectories. We illustrate how they can be found as projective fixed…
For three-dimensional piecewise-smooth systems of ordinary differential equations, this paper characterises the stability of points that belong to a switching surface and are equilibria of exactly one of the two neighbouring pieces of the…
This paper investigates the coplanar and circular three-body problem in the parametrized post-Newtonian (PPN) formalism, for which we focus on a class of fully conservative theories characterized by the Eddington-Robertson parameters…
Results on the problem of stabilizing a nonlinear continuous-time system by a finite number of control or measurement values are presented. The basic tool is a discontinuous version of the so-called semi-global backstepping lemma. We derive…
We are concerned with the problem of determining the nonlinear term in a semilinear elliptic equation by boundary measurements. Precisely, we improve [5, Theorem 1.3], where a logarithmic type stability estimate was proved. We show actually…
Solutions to the collinear three-body problem which do not end in triple collision pass through an infinite number of binary collisions. Given three masses, we show that four geometric quantities generate a finite description of itineraries…
In this paper we classify the central configurations of the circular restricted 4-body problem with three primaries at the collinear configuration of the 3-body problem and an infinitesimal mass. The case where the three primaries have the…
The possible observations of Trojan-like extrasolar planets stimulate the deeper understanding of the stability behaviour of the co-orbital resonant motion. By using Hill's equations and the energy-rate method an analysis of the stability…
In the framework of the planar restricted three body problem we study a considerable number of resonances associated to the Kuiper Belt dynamics and located between 30 and 48 a.u. Our study is based on the computation of resonant periodic…
We study smoothness of generalized solutions of nonlocal elliptic problems in plane bounded domains with piecewise smooth boundary. The case where the support of nonlocal terms can intersect the boundary is considered. We find conditions…
The elliptic restricted three body problem has been well studied. However, the previous formulations of the problem have used a rotating coordinate system to keep the positions of the primary and secondary on the x-axis. This requires the…