Dynamics of a variable-mass, flexible-body system

A new formulation of the dynamics of a variable-mass, flexible-body system is presented by extending Kane's equations for variable mass particles to flexible bodies characterized by load-dependent stiffness and assumed modes. The method captures the effects of thrust, mass center change, and changes in transverse vibration frequencies due to mass loss and thrust. An order-n formulation with prescribed motion of a gimballed nozzle Is given for a flexible rocket. Equations for a planar flexible rocket are illustrated and solved numerically. Open-loop simulations with prescribed gimbal motion show that the difference in large motion Right behavior between a rigid-body model and a flexible-body model of a rocket increases as the flexibility increases, Changes in bending frequencies of a flexible rocket due to mass loss and thrust-induced softening are shown.