# Modeling and Control of an Articulated Multibody Aircraft
## 1 Introduction
### Related Work
#### 1.1.2 Moving-Mass Control in Spacecraft and Aircraft  
Mass distribution plays an important role in vehicle dynamics, and varying the vehicle's mass distribution affects the system's dynamics, stability and balance [52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62]. In the early days of aviation, pilots would modify their body posture, thus moving the aircraft's center of mass to accomplish control or stability [63; 64]. The concept is of primary importance in the control of hang-gliders [7]. In [65], [PERSON] and [PERSON] designed an attitude control system for a transatmospheric missile using three internal moving masses. Each mass was able to move along its respective axis to change the attitude of the missile. Simulation results showed the method was able to effectively control the missile, achieving static stability and attitude control. Other applications for missile control can be found in [66; 67]. [PERSON] and [PERSON] [68; 69; 70] developed a seven-degree-of-freedom (7 DoF) flight dynamics model for trajectory control of a projectile with an internal translating vibrating mass to study the potential of this control mechanism. Significant control authority was achieved with a mass of about 1% of the total projectile mass by vibrating the mass normal to the axis of symmetry and at the roll rate frequency. Nonlinear equations of a spinning vehicle with two internal moving elements were derived by [PERSON] et al. [71] to investigate the use of linearly moving-mass actuators for trajectory control. Results showed that the moving-mass controller was able to effectively control the vehicle's trajectory. [PERSON] et al. [72] investigated a stratospheric airship with various control systems, including traditional aerodynamic control surfaces, vector thrust, ballonet, and moving mass. One mass moved laterally, controlling roll angle, while the other moved longitudinally to regulate pitch angle. The results showed that moving-mass control (MMC) outperformed control surfaces, since the moving masses had no effect on the drag of the airship. The use of internal moving masses for flight control in SUAVs has also been demonstrated. [PERSON] [36] was able to demonstrate the use of translational internal moving masses as a feasible alternative moment generation mechanism to conventional aerodynamic control surfaces for SUAVs. Another study by [PERSON] [73] showed through flight test that without airelons, a small unmanned airplane was able to control roll using two laterally moving internal masses. Moving-mass control has been implemented in rotorcraft as well. For the control of a large quadrotor, [PERSON] et al. [74; 75] implemented four translational movable masses in the quadrotor's four arms to change the center of gravity and control the pitch and roll of the craft. [PERSON] [76] used MMC for passive roll and pitch stabilization of an indoor coaxial helicopter. The mechanism involved the use of two semi-circular guides for mass movement. A study presented by [PERSON] [77] successfully implemented a spherical moving-mass steering mechanism to improve the passive stability of a mini-coaxial helicopter in hover. The most effective techniques for managing spacecraft center of mass (CoM) and attitude trajectory are reaction forces and torques, using internal mass ejection and rotating masses. Command torques are also generated by reaction forces that do not pass through the CoM. As such, only propulsion, orbit and attitude control can be achieved [78]. Rotating masses, on the other hand, produce a variation in angular momentum in any direction,consequently commanding a torque for attitude control [78]. The masses are rotated by electric motors and the corresponding actuators are either fixed-axis variable-speed motors (reaction wheels) or control moment gyros with gimbaled fixed-speed motors that may be oriented in any desired direction. At low orbital altitudes of less than about 450 km, spacecraft suffer from aerodynamic disturbances.