On the stability of a body with connected moving parts.

This paper presents several general propositions and examples relating to the of bodies with holonomically constrained moving (e.g., gravity gradient-stabilized satellites, spin-stabilized space vehicles). The system may be a combination of particles, bodies, and continuous bodies with internal damping between the parts. Stability of is discussed using theorems based on the direct method of Lyapunov. Stability is proved to depend on the positive definite property of a certain easily constructed (potential) function of the generalized coordinates; asymptotic is demonstrated in the case of complete damping. A theorem on quadratic forms is used to give qualitative conditions under which an equilibrium position of a general system of bodies is stable if the system possesses rigid body stability and if the parts motion is stable. As an example, the of a free, internally damped, quasi-rigid body is discussed; the phenomenon of convergence of the axis of maximum moment of inertia to the axis of total (equilibrium) angular momentum is examined critically in the light of the theory presented. The general theory is applicable to nonlinear systems, and it gives bounds on the configuration-space convergence region.