Effects of transverse bending on the motion of free-flight rockets

Two models for a transversely flexible, thrusting, free-flight rocket are presented. The first model consists of two rigid bodies connected so that relative transverse rotations of the bodies are resisted by linear restoring and damping torques. Equations of motion, both nonlinear and linear, for unconstrained motion are derived. No aerodynamic forces or moments are included in the models. Solutions to the linear equations for constant rocket spin rate are obtained in closed form and used to obtain results for a baseline rocket and parametric variations thereof. These results indicate that transverse flexibility contributes significantly to rocket mallaunch when the spin rate is high, since the long-period part of the angular rate at launch is directly proportional to spin rate and to the magnitude of transverse deformation. Effects of thrust misalignment are considered in comparing results obtained from solutions to the linear equations with flight data for a particular rocket. Equations of motion of the two-body rocket on a 'rigid' (non-moving) launcher are also derived. Results obtained by numerically integrating these equations are presented. The second and more complex model is that of a continuous, non-uniform, slender rod subject to 'internal' thrust.