The paper investigates the stability of a nonlinear dissipative mechanical system subjected to potential forces, gyroscopic forces, Rayleigh damping and circulatory forces, using direct Liapunov method. Assuming the gyroscopic matrix depends on a parameter, two asymptotically stable theorems are obtained, and the lower bounds of the parameter are evaluated.

The paper investigates the stability of mechanical systems subjected to potential forces, gyroscopic forces, circulatory forces and Rayleigh damping, by means of the Rayleigh quotients. Two stability theorems are obtained. Stability criterions are described by the gyroscopic, circulatory and Rayleigh damping matrices.

In this paper, stability of a complex spacecraft is studied by the use of two new models. The rst, is a rigid-flexible model, which consists of a rigid body and a deploying flexible beam; while the second, includes a liquid lled rigid body with a deploying flexible beam. In particular, the deploying beam in both models is assumed to have a nite deflection pro le. It has been proved that nonlinear transverse vibrations of a beam are stable when undergoing uniform extension or retrieval

The paper investigates the stability of linear non-conservative mechanical systems subjected to potential, gyroscopic. circulatory forces and Rayleigh damping. Three stability theorems are proved by means qf the Rayleigh quotients. The stability criterions given by tile theorems are convenient and useful because they are independent of the Rayleigh quotients.

To describe the relative motion of spacecraft formation flying, this paper presents a method based on relative orbital elements, which is suitable to elliptical orbit with arbitrary eccentricity. The long time formation flying conditions are theoretically derived taken into account the relationship between relative motion and relative orbital elements. These conditions include that both the orbital periods of all participating spacecrafts should be the same and other relative orbital elements should be small enough. The expected relative distance of the spacecrafts would determine the magnitudes of such relative orbital elements. Theoretical analysis and numerical simulation results show that the spacecrafts with sufficient small relative orbital elements can keep long time formation flying without any active control when the orbital perturbations are not considered. The results also show that Hill’s equation is only suitable for describing a short time formation flying.