Attenuation control of gyrostat without energy supply

Abstract

The motion by inertia of a system of two rigid bodies connected by a cylindrical hinge is considered. One of the bodies (platform) is arbitrary, and the second (rotor) is dynamically symmetrical, and the symmetry axis coincides with the hinge axis. The system does not possess any actuator capable of controlling the angular velocity of the rotor. As a control element, a “trigger” is used that prevents the relative rotation of the rotor. In the absence of external moments, the system initially moves about the center of mass as a rigid body in the case of Euler. After the rotor is released, it begins to rotate in such a way that the projection of its absolute angular velocity on the axis does not change. At that moment, when the relative rotation speed goes to zero, the latch can be turned on without losing energy. As a result, the original trajectory of the body changes. The possibilities of platform overturning and stopping its “tumbling” are studied.Previously, such systems (gyrostats) have been widely used to control the orientation of satellites or mobile robots. In most cases, the presence of a motor that changes the energy of the system was assumed. Unpowered gyrostats were used to stabilize the equilibrium orientations. Latched systems with two modes of motion do not appear to have been previously studied. The theory presented in this paper can be used to control the orientation of satellites or robots.