MAE146: Astronautics – HomeworkAssigned: Wednesday, January 6th,2010Due date: Friday , January 8th,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 forgetto write your name on your copy to receive credit.Problem 1 (10pts): Elementary rotationsGiven a reference frameR= (0,ˆe1,ˆe2,ˆe3), the elementary rotations are defined as the rotations transforming thebasis ( ˆe1,ˆe2,ˆe3) into a basis (ˆf1,ˆf2,ˆf3) with one of the basis vector fixed (that isˆfi= ˆeifor some indexi). The otherbasis vectors are rotated by a fixed angle,θ, with positive angle being understood as counter-clock-wise rotationswhen looking down the fixed vector.For example, the rotation leaving the 3rdaxis fixed is defined by the relations:ˆf1=cos(θ).ˆe1+ sin(θ).ˆe2(1)ˆf2=-sin(θ).ˆe1+ cos(θ).ˆe2(2)ˆf3=ˆe3(3)or, expressed in matrix form:ˆf1ˆf2ˆf3=R3(θ).
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Geographic coordinate system, ECF, Coordinate system, Polar coordinate system