In the presence of noncompact symmetry, the stability of relative equilibria under momentum-preserving perturbations does not generally imply robust stability under momentum-changing perturbations. For axisymmetric relative equilibria of Hamiltonian systems with Euclidean symmetry, we investigate different mechanisms of stability: stability by energy-momentum confinement, KAM, and Nekhoroshev s...

Stability analysis in compliant mechanism (CM) design is of utmost importance. From a practical point of view, a CM that is unstable is of no significance (has no practical value). Three useful plots were considered in the evaluation of each of the dynamic models of nine configurations of compliant constant-force compression mechanisms (CCFCMs) for their stability characteristics, which include...

Children are increasingly born into cohabiting parent families, but we know little to date about the implications of this family pattern for children’s lives. We examine whether children born into premarital cohabitation and first marriages experience similar rates of parental disruption, and whether marriage among cohabiting parents enhances union stability. These issues are important because ...

We study the linear and nonlinear stability of relative equilibria in the planar n-vortex problem, adapting the approach of Moeckel from the corresponding problem in celestial mechanics. After establishing some general theory, a topological approach is taken to show that for the case of positive circulations, a relative equilibrium is linearly stable if and only if it is a nondegenerate minimum...

A mechanical system with perfect constraints can be described, under some mild assumptions , as a constrained Hamiltonian system (M; ; H; D; W): (M;) (the phase space) is a symplectic manifold, H (the Hamiltonian) a smooth function on M, D (the constraint submanifold) a submanifold of M, and W (the projection bundle) a vector sub-bundle of T D M, the reduced tangent bundle along D. We prove tha...

n this article, a new graphical tool called the phase-root locus is introduced. It is the dual of the conventional root locus, and indicates the motion of closed-loop poles in the s-plane as phase is added to the open-loop transfer function. The root locudphase-root locus plots will be shown to facilitate destabilization diagnosis, which may help determine what part of an unstable physical syst...