Abstract
Chetaev [1] has investigated the motion of a heavy unbalanced gyroscope on gimbals with the vertical axis of the outer ring. The stability of certain stationary solutions of such a motion has been investigated by Skimel [2], Magnus [3] and Rumiantsev [4]. Similar investigations for the horizontal axis of the outer ring have been carried out by Rumiantsev [5]. Bogoiavlenskii [6] obtained in the latter case a particular integral of the equations of motion. This paper investigates the motion of a symmetric unbalanced gyroscope on gimbals when the axis of the outer ring makes any angle with the vertical [7], examines stability of certain stationary solutions and derives a particular solution when the axis of the outer ring is horizontal.
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