Coupled-Interaction Launch Behavior of a Flexible Rocket and Flexible Launcher

A numerical solution is developed for analyzing the coupled dynamic interaction behavior of a thrust-loaded flexible spinning rocket propelled along a flexible launcher. The partial differential equations of motion describing the dynamic behavior of the system are solved using a hybrid approach. The spatial behavior of the rocket is modeled by the finite-element method as a beam column with sectionally constant cross-section properties, while a summation of the natural mode solutions are used to model the spatial behavior of the launcher. The resulting time-dependent differential equations, which are coupled together by consideration of the time-dependent support forces between the rocket and the launcher, are then numerically integrated in time to obtain the system transient dynamic response. Numerical results are presented which demonstrate the validity of the method and which demonstrate the influence of rocket and launcher bending flexibility on rocket launch attitude and, hence, rocket accuracy. The bending effects are shown to significantly increase unfavorable rocket launch conditions.