HW1 - MAE146: Astronautics Homework Assigned: Wednesday,...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
MAE146: Astronautics – Homework Assigned: Wednesday, January 6 th , 2010 Due date: Friday , January 8 th , 2010, (at the beginning of the lecture) Please justify all of your answers. Write your answer cleanly with sentences and diagrams to explain. Don’t forget to write your name on your copy to receive credit. Problem 1 (10pts): Elementary rotations Given a reference frame R = (0 , ˆ e 1 , ˆ e 2 , ˆ e 3 ), the elementary rotations are de±ned as the rotations transforming the basis ( ˆ e 1 , ˆ e 2 , ˆ e 3 ) into a basis ( ˆ f 1 , ˆ f 2 , ˆ f 3 ) with one of the basis vector ±xed (that is ˆ f i = ˆ e i for some index i ). The other basis vectors are rotated by a ±xed angle, θ , with positive angle being understood as counter-clock-wise rotations when looking down the ±xed vector. For example, the rotation leaving the 3 rd axis ±xed is de±ned by the relations: ˆ f 1 = cos( θ ) . ˆ e 1 + sin( θ ) . ˆ e 2 (1) ˆ f 2 = - sin( θ ) . ˆ e 1 + cos( θ ) . ˆ e 2 (2) ˆ
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/13/2010 for the course MAE 19100 taught by Professor Villac during the Winter '10 term at UC Irvine.

Ask a homework question - tutors are online