Title page for ETD etd-04282004-071227

Type of Document Dissertation
Author Berry, Matthew M.
Author's Email Address maberry2@vt.edu
URN etd-04282004-071227
Title A Variable-Step Double-Integration Multi-Step Integrator
Degree PhD
Department Aerospace and Ocean Engineering
Advisory Committee
Advisor Name Title
Hall, Christopher D. Committee Chair
Healy, Liam Committee Member
Johnson, Lee W. Committee Member
Schaub, Hanspeter Committee Member
Woolsey, Craig A. Committee Member
  • Orbit Determination
  • Orbit Propagation
  • Variable-Step Integration
  • Numerical Integration
Date of Defense 2004-04-16
Availability unrestricted
A new method of numerical integration is presented here, the variable-step Stormer-Cowell method. The method uses error control to regulate the step size, so larger step sizes can be taken when possible, and is double-integration, so only one evaluation per step is necessary when integrating second-order differential equations. The method is not variable-order, because variable-order algorithms require a second evaluation.

The variable-step Stormer-Cowell method is designed for space surveillance applications,which require numerical integration methods to track orbiting objects accurately. Because of the large number of objects being processed, methods that can integrate the equations of motion as fast as possible while maintaining accuracy requirements are desired. The force model used for earth-orbiting objects is quite complex and computationally expensive, so methods that minimize the force model evaluations are needed.

The new method is compared to the fixed-step Gauss-Jackson method, as well as a method of analytic step regulation (s-integration), and the variable-step variable-order Shampine-Gordon integrator. Speed and accuracy tests of these methods indicate that the new method is comparable in speed and accuracy to s-integration in most cases, though the variable-step Stormer-Cowell method has an advantage over s-integration when drag is a significant factor. The new method is faster than the Shampine-Gordon integrator, because the Shampine-Gordon integrator uses two evaluations per step, and is biased toward keeping the step size constant. Tests indicate that both the new variable-step Stormer-Cowell method and s-integration have an advantage over the fixed-step Gauss-Jackson method for orbits with eccentricities greater than 0.15.

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