We consider the spatial restricted three body problem RTBP for values of the mass parameter close to Routh We analyse the dynamics around the vertical peri odic orbits which are born at the equilateral equilibrium points L and L and we describe the con nement around the complex unstable periodic orbits due to the D stable and unstable invariant manifolds

In this paper the motion without sliding of a homogeneous ball on a surface of revolution is studied. It is shown that the necessary condition for stability of stationary periodic motions of the ball obtained by Routh is also a sufficient one. We prove that the nondegenerate invariant manifolds are diffeomorphic to unions of invariant tori filled with quasiperiodic motions.

Simple proofs of the Hermite–Biehler and Routh–Hurwitz theorems are presented. The total nonnegativity of the Hurwitz matrix of a stable real polynomial follows as an immediate corollary. © 2003 Elsevier Inc. All rights reserved. AMS classification: 93D05; 34D99; 12D10; 26C05; 26C10; 30C15; 15A23; 15A48; 15A57

This paper presents a trajectory tracking control method for flexible space robot. The advantage of the method is that it is free from spill-over instability as it uses a robust overwhelming trajectory controller. The proposed controller is conceptualized for a single rotational degree of freedom case. The efficacy of the scheme is illustrated by simulation results. The stability analysis of th...

We study the dynamics of the relative motion of satellites in the gravitational field of the Earth, including the effects of the bulge of the Earth (the J2 effect). Using Routh reduction and dynamical systems ideas, a method is found that locates orbits such that the cluster of satellites remains close with very little dispersing, even with no controls. The use of controls in the context of thi...

The results of two kinds of studies show PA develops on its own in first language development, without instruction: (1) children in comparison groups in PA training studies, who get no PA training, typically improve in PA (Ehri, Nunes, Willows, Schuster, Yaghoub-Zadehm and Shanahan, 2001, p. 276); (2) longitudinal studies show that nearly all children score very well on tests of PA by about gra...

This paper will review recent advances in the formulation of a discrete version of geometric mechanics, based on the discretization of Hamilton’s variational principle, and progress that has been made in reduction theory for discrete variational mechanics in the form of Discrete Routh Reduction. To place discrete geometric mechanics on a firm mathematical foundation, we propose to develop a dis...