Static Response of a Multiple Launch Rocket System During Launch Using Linear Multibody System Transfer Matrix Method

The mass and its distribution of a multiple launch rocket system (MLRS), from which rockets shoot successively, vary continuously during the firing. The system response comprises a static response caused by gravity changes leading to the deviation from an initial equilibrium configuration (EC) to a current EC, and a dynamic response relative to the current EC. The simulation results of launch dynamics and firing precision will diverge from reality if the change of the system’s EC is ignored throughout the firing process. Thus, it is crucial to accurately and rapidly calculate the static response of an MLRS during firing. In this work, the static response due to the mass changes of an MLRS during the firing process is studied using the linear multibody system transfer matrix method (MSTMM). To consider the change of mass and its distribution of the pitching part caused by the shot rockets, an equivalent force-system model is proposed. The static response of the system due to the change of mass can be attributed to the static response of the original system subjected to the additional force system, which can be obtained by using the linear MSTMM to compute the steady-state response of the original system with the excitation frequency of the additional force system being zero. The proposed method can fast compute the static response (both position and orientation) of each body element due to the mass change. It also provides a theoretical basis for accurate computation of the launch dynamics of a multibody system.