Abstract
This article details a scheme for evaluating the stability of motions of a system consisting of a rigid body connected at one point to a rotating arm. The nonlinear equations of motion for the system are formulated, and a method for finding exact solutions representing motions that resemble a state of rest is presented. The equations are then linearized and roots of the eigensystem are classified and used to construct stability diagrams that facilitate the assessment of effects of varying the body's mass properties and system geometry, changing the position of the attachment joint, and adding energy dissipation in the joint.
Highlights
Because it is widely thought that it may be harmful to humans to be in a state of weightlessness for extended periods of time, various schemes for creating an artificial gravity environment for astronauts are currently under investigation. Most of these involve exploitation of the basic fact that underlies the operation of a centrifuge, namely, that each point of a rigid body that is in a state of rotation about an axis fixed both in the body and in an inertial reference frame possesses an acceleration directed toward the axis of rotation
Because spaceflight structures are required to be relatively light and the dimensions of a rotating space-centrifuge must be large to provide a comfortable living environment, analyses of realistic systems generally involve motions more complicated than those of a single rigid body in a state of simple rotation, such as those performed by two rigid bodies connected by an elastic tether (Robe and Kane, 1967)
We consider the motion of a rigid body attached by means of a ball-and-socket joint to a rigid arm that is rotating with constant angular speed about an axis fixed in a Newtonian reference frame
Summary
Because it is widely thought that it may be harmful to humans to be in a state of weightlessness for extended periods of time, various schemes for creating an artificial gravity environment for astronauts are currently under investigation. Most of these involve exploitation of the basic fact that underlies the operation of a centrifuge, namely, that each point of a rigid body that is in a state of rotation about an axis fixed both in the body and in an inertial reference frame possesses an acceleration directed toward the axis of rotation.
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