[ugrads] [Mathclub-members] Math Club Talk 11/13 - Rotation Frame Change Of Particle Flux Environment Using Quaternions

IIT Math Club mathclub at iit.edu
Sun Nov 11 13:09:21 CST 2012

Dear Math Club members,

We'll be having our next Math Club Talk this Tuesday, November 13th at 12:40pm in Engineering 1 room 102.

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

Also, at the beginning of the meeting we will talk about an exciting new course we are starting for next semester on the Wolfram Mathematica software. More information will be presented during the meeting.

Pizza and refreshments will be served!

Hope to see you there,


Luis Larco
IIT Math Club
mathclub at iit.edu

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