Limit motions of a slightly asymmetric reentry vehicle acted on by cubic damping moments

Although the linear damping moment on a symmetric missile is the same for planar motion as for coning motion, nonlinear damping for these different motions is not necessarily the same. The general cubic nonlinear damping expression requires the use of two coefficients and such damping can cause either circular or planar limit motion. The addition of configurational asymmetry introduces the possibility of more complicated limit motion. The existence of one-, two- and three-mode stable limit motions is studied by quasi-linear analysis and the results verified by numerical integration of the exact differential equation.