Multibody Parachute Flight Simulations Using Singular Perturbation Theory

A method has been developed to reduce the numerical stiffness and processing requirements of high fidelity entry trajectory models involving parachutes. Parachute deployment systems have often been simulated using rigid body dynamic models. The system is comprised of a parachute rigid body attached to the vehicle via a confluence mass with flexible lines. The simulations incorporating the confluence mass often take excessive amounts of processing time due to the relatively small mass of the confluence point and the resulting high frequency motion. The method introduced here, known as singular perturbation theory, involves suppressing the small inertia responsible for this motion. The singularly perturbed system allows simplification of the equations of motion by removing the confluence point velocity state equations, thereby increasing the time step and decreasing overall processing time. The singular perturbation method is applied to parachute entry models of the Mars Exploration Rover mission as well as the Crew Exploration Vehicle abort mode. Results from these tests are compared to models where a confluence point with mass was used to assess the validity and efficiency of the method.