Linear stability of ring systems with generalized central forces

Linear Stability of Ring Systems Around Oblate Central Masses

In this paper, we consider the stability of a ring of bodies of equal mass uniformly distributed around a large oblate central mass. The purpose of this and previous papers is to shed light on the stability of Saturn’s rings. Previous papers have been limited by the assumptions that (1) all ring bodies are at the same distance from the central body, (2) the central body acts like a point mass (...

Linear Stability of Ring Systems

We give a self-contained modern linear stability analysis of a system of n equal mass bodies in circular orbit about a single more massive body. Starting with the mathematical description of the dynamics of the system, we form the linear approximation, compute all of the eigenvalues of the linear stability matrix, and finally derive inequalities that guarantee that none of these eigenvalues hav...

Exponential Stability of Linear Systems with Multiple Time Delays

In this paper, a class of linear systems with multiple time delays is studied. The problem of exponential stability of time-delay systems has been investigated by using Lyapunov functional method. We will convert the system of multiple time delays into a single time delay system and show that if the old system is stable then the new one is so. Then we investigate the stability of converted new ...

Cauchy-Rassias Stability of linear Mappings in Banach Modules Associated with a Generalized Jensen Type Mapping

Generalized matrix diagonal stability and linear dynamical systems

Let A = (aij ) be a real square matrix and 1 p ∞. We present two analogous developments. One for Schur stability and the discrete-time dynamical system x(t + 1) = Ax(t), and the other for Hurwitz stability and the continuous-time dynamical system ẋ(t) = Ax(t). Here is a description of the latter development. For A, we define and study “Hurwitz diagonal stability with respect to p-norms”, abbrev...