Dynamics of Gyroscopic Systems for Indicating the Vertical on Ships

Abstract

Knowledge of vertical direction on ships is of importance for many applications. M.Schuler was the first who had proposed the use of gyroscopic systems for indicating the vertical. A.Yu.Ishlinsky obtained the conditions for the ideal performance of the raumcompass and developed its theory. In the paper the following theorem is proved : the line connecting the suspension point and the mass center of an arbitrary gyroscopic system is always directed along the vertical if and only if the vector of the angular momentum of the system in absolute motion about the suspension point is constant in inertial space. This theorem provides the conditions for the unperturbable gyroscopic systems. The analogy between various unperturbable systems is established. The known studies of the unperturbable systems are connected with a case when the value of system angular momentum is zero. The paper presents the investigation for the case when the system angular momentum is constant in inertial space and not zero. The equations of motions for a new class of unperturbable systems are derived and their motion is investigated. In particular it is shown that the systems studied have both Schuler’s period and other periods of oscillations which depend upon the value of angular momentum.