Application of the Simple Pendulum Model to Incorporate Propellant Slosh Dynamics in 6-DoF Launcher Flight

The coupled rigid-body/slosh/elasticity dynamics equations are developed for 6-DoF flight of launchers. The equations of motion are derived by means of Lagrange’s equations in terms of quasi-coordinates and alternatively in the inertial frame. The simple pendulum model for planar motion is extended to model slosh dynamics in 6-DoF flight and the elastic motion is represented in terms of modal displacement coordinates relative to the elastic mean axes system. It is shown that this model is consistent with the simpler model for planar motion which has been developed in previous studies. The proposed dynamics model is incorporated in conjunction with the models for the other subsystems in a MATLAB/Simulink program to simulate 6-DoF flight of launchers.