Discovering Method of Control of the "Dzhanibekov's Effect" and Proposing its Applications for the Possible Future Space Missions

Abstract

This paper is dedicated to the numerical simulation and analysis of the "Dzhanibekov's Effect" - non-stable "flipping" motion of the rigid body with periodic change by 180° of the direction of the main axis of its rotation, always occurring when the body is provided with the main rotation about its axis with intermediate principal moment of inertia. In this work we are proposing and developing a new concept of "inertial morphing" of the spacecraft for the versatile control of the "Dzhanibekov's Effect", enabling manipulations with the attitude of the spacecraft without employing classical gyroscopes. We are demonstrating that applying controlled changes to the inertial properties of the system, the "Dzhanibekov's Effect" flipping motion can be completely stopped, if this motion is undesirable. Similarly, the "Dzhanibekov's Effect" flipping motion can be activated on the stable, non-tumbling spacecraft, if this is desired for the purposes of the mission. We are also showing that the frequency of the flipping motion can be controlled within a wide range. For the implementation of the transformations between stable and unstable modes of motion, we are proposing two main conceptual solutions, involving changes to the system, resulting in the intermediate moment of inertia becoming the smallest or largest principal moment of inertia of the body. Development of the conceptual 6-mass model of the spacecraft enabling controllable switching OFF of the "Dzhanibekov's Effect" flipping is presented. Furthermore, we also exploring the possibilities of utilization of the "Dzhanibekov's Effect" for possible future new space missions, employing periodic change in the attitude orientation of the spacecraft. It is believed, that new results of this research may have multiple applications for possible future space missions. In particular, we are suggesting assistance in establishing formation flight; thruster direction control and control of the period of the "flipping" motion of the spacecraft.