Aerospace Engineering Research Works
Permanent URI for this collectionhttp://hdl.handle.net/1903/1655
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Item A Variable-Step Double-Integration Multi-Step Integrator(Univelt, Inc., 2004-02) Berry, Matthew M.; Healy, Liam M.A variable-step double-integration multi-step integrator is derived using divided differences. The derivation is based upon the derivation of Shampine-Gordon, a single-integration method. Variable-step integrators are useful for propagating elliptical orbits, because larger steps can be taken near apogee. As a double-integration method, the integrator performs only one function evaluation per step, whereas Shampine-Gordon requires two evaluations per step, giving the integrator a significant speed advantage over Shampine-Gordon. Though several implementation issues remain, preliminary results show the integrator to be effective.Item Accuracy and Speed Effects of Variable Step Integration for Orbit Determination and Propagation(Univelt, Inc., 2003-08) Berry, Matthew M.; Healy, Liam M.In this paper the fixed step Gauss-Jackson method is compared to two variable step integrators. The first is the variable step, variable order Shampine-Gordon method. The second is s-integration, which may be considered an analytical step regulation. Speed tests are performed for orbit propagation with the integrators set to give equivalent accuracy. The integrators are also tested for orbit determination, to determine the speed benefit of the variable step methods. The tests give an indication of the types of orbits where variable step methods are more efficient than fixed step methods.Item The generalized Sundman transformation for propagation of high-eccentricity elliptical orbits(Univelt, Inc., 2002-01) Berry, Matthew M.; Healy, Liam M.A generalized Sundman transformation dt = cr^n ds for exponent n >= 1 may be used to accelerate the numerical computation of high-eccentricity orbits, by transforming time t to a new independent variable s. Once transformed, the integration in uniform steps of s effectively gives analytic step variation in t with larger time steps at apogee than at perigee, making errors at each point roughly comparable. In this paper, we develop techniques for assessing accuracy of s-integration in the presence of perturbations, and analyze the effectiveness of regularizing the transformed equations. A computational speed comparison is provided.