Approximate Solution to the Angular Speeds of a Nearly-Symmetric Mass-Varying Cylindrical Body

Angular momentum of free variable mass systems is partially conserved

“…where the first term on the right-hand side of Equation (17) evaluates to zero since n h is fixed in Q . Then, substituting for ω Q from Equation (16) in Equation (17) gives…”

“…A control volume approach [8,9] to account for continuous mass variation subsequently emerged which has since become the modeling standard amongst the community of researchers on rocket flight dynamics. Recent work using the control volume formulation has focused on equation of motion formulation for general variable mass systems [10,11], modeling and analysis of rocket-type systems [12][13][14][15] and an abstraction of the rocket problem [16], and stability of transverse rotational motion in solid rocket motors [17]. The developments presented here on angular momentum also utilize this control volume formulation.…”

Geometry of motion and nutation stability of free axisymmetric variable mass systems

“…A limitation of some of these studies on variable mass systems [13,15,19] is that stability information is heuristically interpreted by examining the evolution of the angular velocity. This paper develops an alternative graphical approach to assess the coning motion by generating a solution to the second Euler angle.…”

“…More recently, Ha and Janssens [18] investigated the CONTOUR mishap using an identical model for mass variation as the aforementioned papers. As the CON-TOUR spacecraft exhibits slight variations in its transverse moments of inertia, an approach to analytically determine the angular speeds of such a nearly-symmetric system with mass loss has recently been developed and numerically validated [19].…”