Arbitrary Controlled Re-Orientation of a Spinning Body by Evolving its Tensor of Inertia

TL;DR

This paper presents a novel method for controlling the orientation of a spinning body by optimally evolving its tensor of inertia, enabling complex, propellant-free re-orientation maneuvers demonstrated through simulations.

Contribution

It introduces an optimal control approach to manipulate a body's tensor of inertia for arbitrary re-orientations, including complex maneuvers using intermediate axis instability.

Findings

Achieves desired orientation stabilization without propellants

Enables arbitrarily complex re-orientation trajectories

Demonstrates effectiveness through numerical simulations

Abstract

Bodies with the nonspherical tensor of inertia exhibit a variety of rotational motion patterns, including chaotic motion, stable periodic (quasi-periodic) rotation, unstable rotation around the direction close to the body's second principal axis, featuring a well-known tennis-racket (also known as Garriott-Dzhanibekov) effect -- series of seemingly spontaneous 180 degrees flips. These patterns are even more complex if the body's tensor of inertia (TOI) is changing with time. Changing a body's TOI has been discussed recently as a tool to perform controllable Garriott-Dzhanibekov flips and similar maneuvers. In this work, the optimal control of the TOI of the body (spacecraft, or any other device that admits free rotation in three dimensions) is used as a means to perform desirable re-orientations of a body with respect to its angular velocity. Using the spherical TOI as the initial and final point of the maneuver, we optimize the parameters of the maneuver to achieve and stabilize the desired orientation of the body's principal axes with respect to spin angular velocity. It appears that such a procedure allows for finding arbitrarily complex maneuver trajectories of a spinning body. In particular, intermediate axis instability can be used to break the alignment of the body's principal axis and the axis of rotation. Such maneuvers do not require utilization of propellants and could be straightforwardly used for attitude control of a spin-stabilized spacecraft. The capabilities of such a method of angular maneuvering are demonstrated in numerical simulations.