The necessary and sufficient condition for the stability of a rigid body

Abstract

In this paper, the stability of the unperturbed rigid body motion close to conditions, related with the center of mass, is investigated. The three first integrals for the equations of motion are obtained. These integrals are used to achieve a Lyapunov function and to obtain the necessary and sufficient condition satisfies the stability criteria.

The Stability Conditions for a Heavy Solid Motion

“…We deduce from the relations in ( 12) that L i > 0, i � 1, 2, 3, if and only if the following inequalities are satisfied [14], respectively:…”

“…e permanent orbiting stability problem of an asymmetric gyro is considered in [13] when the gyro moved under a Newtonian force field. In [14], the author considered the conditions of stability motion of a rigid body rotating about the x-axis when I 1 > I 2 > I 3 . He assumed a moment λ 1 about the x-axis and deduced the equations of motion.…”

The Slow Spinning Motion of a Rigid Body in Newtonian Field and External Torque

“…e advantage of this method is as follows: assuming low energy at the initial instant instead of high energy, obtaining a slow periodic motion instead of a fast periodic one, and giving the solutions in a new domain of motion r o ⟶ 0 and ε ⟶ ∞. e case when A < B < C [21] cannot be solved here since ω ′ 2 is negative in this case. So we will treat this case separately in the future, in shaa Allah.…”