Global Stability of a Shielded Dual-Spin Satellite

Sufficient conditions for the global stabilities of equilibrium positions of a dual-spin satellite equipped with a cylindrical electrostatic screen normal to the circular equatorial orbital plane system under the action of moments induced by the gravitational and Lorentz forces are obtained by Liapunov's direct method. The problem is then studied with respect to all variables, including the angular velocity of the rotor. The instabilities of the problem are solved by the first approximation theorem. Furthermore, sufficient conditions for the global stability of rotation with arbitrary angular velocity for an axisymmetric dual-spin satellite equipped with an electrostatic screen are presented by applying Liapunov's direct method.

Dynamic Stability of Elastic Rotor-Bearing Systems via Liapunov’s Direct Method

A general method of analysis based on Liapunov’s direct method is presented for studying the dynamic stability of elastic rotor-bearing systems. A model comprised of a continuous elastic shaft mounted on two 8-coefficient bearings is used to develop closed-form (series) stability criteria involving system stiffness and damping parameters. It is quantitatively shown by means of graphs how the instability regions are reduced by (a) increasing the shaft dimensionless stiffness parameters, (b) increasing the bearing direct stiffness and damping parameters, and (c) decreasing the bearing cross-coupling stiffness and damping parameters.

Dynamic Stability of Nonlinear Antisymmetrically-Laminated Cross-Ply Rectangular Plates

The dynamic stability problem is solved for rectangular plates that are laminated antisymmetrically about their middle plane and compressed by time-dependent deterministic or stochastic membrane forces. Moderately large deflection equations taking into account a coupling of in-plane and transverse motions are used. The asymptotic stability and almost-sure asymptotic stability criteria involving a damping coefficient and loading parameters are derived using Liapunov’s direct method. A relation between the stability of nonlinear equations and linearized ones is analyzed. An influence on the number of orthotropic layers, material properties for different classes of parametric excitation on stability domains is shown.