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Math Club Talk - Rotation Frame Change Of Particle Flux Environment Using Quaternions

Title: Rotation Frame Change Of Particle Flux Environment Using Quaternions
by Anita E. Thomas
Applied Mathematics, Senior Undergraduate

Meteoroids threaten the safety of spacecraft. Currently, the NASA Meteoroid Engineering Model (MEM) estimates meteoroid flux according to a reference frame derived from the spacecraft (s/c) trajectory, while the NASA “Bumper-ii” code uses a reference frame fixed to the body of the s/c to evaluate damage to the s/c structure. It is therefore cumbersome to relate the environment to the s/c as it changes its trajectory or orientation. My algorithm uses quaternions to rotate a meteoroid flux estimate from MEM’s reference frame to the reference frame used by Bumper. I use quaternions, instead of Euler angles, to avoid singularities. Both algorithms define spheres divided into solid-angle bins surrounding the s/c. Each bin is assigned its respective meteoroid flux, thus creating a flux environment F(θ,φ), where θ and φ are spherical coordinates representing the direction each particle is moving. The environment sphere is then rotated to simulate a s/c orientation change of the opposite rotation. This rotation represents the difference between the MEM coordinate system and the body-fixed s/c coordinate system. Finally, a tally is made of the new (rotated) flux in each s/c flux bin.

Tue Nov 13, 2012 12:40pm – 1:30pm Central Time
Engineering 1 room 102 (map)