Nonlinear Spacecraft Dynamics with a Flexible Appendage, Damping, and Moving Internal Submasses

Chaotic attitude and reorientation maneuver for completely liquid-filled spacecraft with flexible appendage

“…The motion of the tip mass on the appendage is limited to rotation about the e 1 axis and is defined by the angle of twist α. No flexural bending or warping of the connecting rod is permitted, although this type of motion is possible if, for example, the appendage is constrained by a system of guy wires [1]. As a result, motion of the appendage does not shift the center of the system.…”

“…flexible appendages as antennae reflectors and solar arrays [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Numerical results show that the motion of a torquefree spacecraft possesses characteristics common to random, non-periodic solutions due to the energy lost in fuel slosh and flexible appendage vibration.…”

“…Numerical results show that the motion of a torquefree spacecraft possesses characteristics common to random, non-periodic solutions due to the energy lost in fuel slosh and flexible appendage vibration. And this motion, for some sets of system's parameters, was also theoretically proven, by using Melnikov's method, to be chaotic [1][2][3][4][5][6]. As such, the reorientation of the spacecraft relative to the inertially fixed angular momentum vector at the end of the maneuver cannot be determined a priori.…”

“…More recently, Gray et al have used Melnikov's method to detect the presence of chaotic dynamics originating from the saddles of damped satellites. The satellites were subject to small perturbations during an attitude transition maneuver because of the presence of oscillating sub-masses, a flexible appendage limited to torsional vibrations and a rotor immersed in a viscous fluid [1]. By employing Melnikov analytic and numerical methods, the present author studied the chaotic dynamics in an attitude transition maneuver of rigid body with completely liquidfilled cavity in the transition process from minor axis to major axis spin under the influence of viscous damping and small flexible appendages constrained to undergo torsional vibration only [2][3][4].…”

Heteroclinic bifurcations in completely liquid-filled spacecraft with flexible appendage

“…Christopher D. Rahn modeled the spacecraft as a rigid body with a spherical, dissipative fuel slug, presenting a control system that guarantees a final orientation after spin transition [8]. Recently, Gray et al used the Melnikov method to detect the chaotic saddles of damped satellites subject to small perturbations due to small oscillating submasses, a small flexible appendage constrained to undergo only torsional vibration, and a rotor immersed in a viscous fluid in an attitude transition maneuver [9,10]. In their studies, the spherical coordinates were used to transform the equations of motion into a form suitable for the application of the Melnikov method, and analytical criteria for chaotic motion to occur were derived in terms of the system parameters.…”