A Perturbation Technique for Analog Computers

A study of the motion of a fin-stabilized rocket was undertaken to determine the effect of perturbing forces on the trajectory. The mechanization of a complete problem for an analog computer to include small disturbing forces would result in trajectories which are essentially indistinguishable from the ``nominal'' or ``unperturbed'' case because of analog computer accuracy limitations. Instead, the equations of motion for the ``nominal'' case and the ``perturbed'' case, derived by first order ballistic perturbation theory, were solved simultaneously with the nominal solution providing inputs to the perturbed solution. The analog computer solution provided both the nominal trajectory and perturbations from this trajectory. To illustrate the method, the technique is applied to the two-dimensional motion of a rocket in the vertical plane and includes perturbations due to uncertainties in winds, atmospheric density, thrust malalignments, and stability margin.