A new algorithm, Orthogonal Complement Based Divide-and-Conquer Algorithm (O-DCA), is presented in this paper for calculating the forward dynamics of constrained multi-rigid bodies including those topologies involving single or coupled closed loops. The algorithm is exact and non-iterative. The constraints are imposed at the acceleration level by utilizing a kinematic relation between the joint motion subspace (or partial velocities) and its orthogonal complement. Sample test cases indicate excellent constraint satisfaction and robust handling of singular configurations. Since the present algorithm does not use either a reduction or augmentation approach in the traditional sense for imposing the constraints, it does not suffer from the associated problems for systems passing through singular configurations. The computational complexity of the algorithm is expected to be O(n + m) and O(log(n + m)) for serial and parallel implementation respectively, where n is the number of generalized coordinates and m is the number of independent algebraic constraints.
A seven degree-of-freedom (7DOF) dynamic model was developed to provide insight into the flight behavior of Type 200 and other related lightcraft, and to serve as a research tool for developing future engine-vehicle configurations for laser launching of nanosatellites (1–10+kg). Accurate engine, beam, and aerodynamics models are included to improve the predictive capability of the 7DOF code. The aerodynamic forces of lift, drag, and aerodynamic pitching moment were derived from FLUENT® computational fluid dynamics predictions, and calibrated against limited existing wind tunnel data. To facilitate 7DOF model validation, simulation results are compared with video analysis of actual flights under comparable conditions. Despite current limitations of the 7DOF model, the results compared well with experimental flight trajectory data.
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