Enhancement of the attitude dynamics capabilities of the spinning spacecraft using inertial morphing

Abstract

<jats:title>ABSTRACT</jats:title><jats:p>In the previous works by the authors, an efficient method of control of the inversion of the spinning spacecraft was proposed. This method was prompted by the Dzhanibekov’s Effect or Tennis Racket Theorem, which are often seen by many as odd or even mysterious. For the spacecraft, initially undergoing periodic flipping motion, proposed method allows to completely stop these flips by transferring the unstable motion into the regular stable spin. Similarly, the method allows activation of the flipping motion of the spacecraft, which is initially undergoing its stable spin. In this paper, spacecraft designs, which have inertial morphing capabilities, are considered and their advantages are further investigated. For general formulation, the ability of the spacecraft to change its inertial properties, associated with all three principal axes of inertia, are assumed. For simulation of these types of spacecraft systems, extended Euler’s equations are used and peculiar dynamics of the spacecraft is illustrated with a several study cases. Complex spacecraft attitude dynamics manoeuvres, using geometric interpretation, employing angular momentum spheres and kinetic energy ellipsoids, are considered in detail. Contributions of the inertial morphing to the changes of the shape of the kinetic energy ellipsoid are demonstrated and are related to the resultant various feature manoeuvres, including inversion and re-orientation. A method of reduction of the compound rotation of the spacecraft into a single stable predominant rotation around one of the body axes was proposed. This is achieved via multi-stage morphing and employing proposed instalment into separatrices. Implementation of the morphing control capabilities are discussed. For the periodic inversion motions, calculation of the periods of the flipping motion, based on the complete elliptic integral of the first kind, is performed. Flipping periods for various combinations of inertial properties of the spacecraft are presented in a systematic way. This paper discusses strategies to the increase or reduction the flipping and/or wobbling motions. A discovered asymmetric ridge of high periods for peculiar combinations of the inertial properties is discussed in detail. Numerous examples are illustrated with animations in virtual reality, facilitating explanation of the analysis and control methodologies to a wide audience, including specialists, industry and students.</jats:p>

Conjugated 3D Virtual Reality Worlds in Spacecraft Attitude Control

“…Using similar principle, it is possible to design cascaded maneuvers. For example, in [12] we designed the sequence, where the spacecraft performed all-axes inversions "parade". With the simplicity of the required control, involving only exiguous/paltry number of IM control actions, it is believed that the systems with IM could find wide application in autonomous small spacecraft.…”

“…The current work aims to contribute to the application of VR in spacecraft attitude dynamics, in particular, to the systems, enabling "Inertial Morphing (IM)": IM with exiguous/paltry number of IM control actions is a new concept, proposed by the authors in 2017 and applied to the spacecraft attitude control [9,10]. The exiguous control enables swift control, requiring minimized energy and computations, and allows design of the fully autonomous future space missions [11,12].…”

Simulation of the Landing Buffer of a Three-Legged Jumping Robot

“…By adjusting the take-off angle and strength, the researchers increased the robot's tendency to pitch down and made it somersault forward, making it flip to a stable landing attitude [10]. In the literature, a method of controlling the reversal of a rotating spacecraft is proposed [11]. This method is facilitated by the Dzhanibekov effect or the intermediate axis theorem (IAT) [12,13].…”

Physics of a Spinning Object Cyclic Inversion at an Orbital Flight

“…The orbital flights of men in space and their experimental investigations manifested the phenomenon of the rotational and cyclic inversions of the spinning objects. This phenomenon under the condition of the free flight of the spinning object shocked physicists because, at first sight, this effect contradicted the principles of classical mechanics [1][2][3][4]. The physicists and mathematicians of the entire world study this unusual effect [5][6][7][8].…”