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Calculate the rotation matrix, R, if frames {A} and {B} are originally coincident then a) Frame {B} is rotated about X by 30 degrees, then about Y, by 15 degrees, and, finally, about Zby 70 degrees.

Calculate the rotation matrix, R, if frames {A} and {B} are originally coincident then a) Frame {B} is rotated about X by 30 degrees, then about Y, by 15 degrees, and, finally, about Zby 70 degrees.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Please assist with this question. I reviewed the lecture notes that was given and do not understand. Please answer with a detailed explanation. Thank you. I believe there is an easier way to solve this using matlab apparently but I dont know.

I will have an image of the reference slide. 

vapping Rotated Frames - Z-Y-Z Euler Angles Start with frame {B} coincident with a known reference frame {A}. Rotate frame {B} about Z by an angle a Rotate frame {B} about Yg by an angle B Rotate frame {B} about Zg by an angle y Note - Each rotation is preformed about an axis of the moving reference frame (B), other then a fixed reference frame {A}. {A} kkk {B'} cosa Rzyz.(a, B.y) = R₂ (a)R₂(B)R₂ (7) = sina sina 0 cos a cos B 0 sin 0 0 1 0 0 1-sin 3 0 [cos a cos ßcos 7-sin a siny = sin a cos B cosy + cosa siny -sin ßcos y [₁1 12 13 22 23 {B"} = 21 {B"} cosy -siny 0 0 cos y 0 ¹j 0 sin y cos B 0 - cosa cos ß sin y-sin a cos y - sin a cos ß sin y + cos a cos y sin 3 sin y cosa sin sin a sin ß cos B
Transcribed Image Text:vapping Rotated Frames - Z-Y-Z Euler Angles Start with frame {B} coincident with a known reference frame {A}. Rotate frame {B} about Z by an angle a Rotate frame {B} about Yg by an angle B Rotate frame {B} about Zg by an angle y Note - Each rotation is preformed about an axis of the moving reference frame (B), other then a fixed reference frame {A}. {A} kkk {B'} cosa Rzyz.(a, B.y) = R₂ (a)R₂(B)R₂ (7) = sina sina 0 cos a cos B 0 sin 0 0 1 0 0 1-sin 3 0 [cos a cos ßcos 7-sin a siny = sin a cos B cosy + cosa siny -sin ßcos y [₁1 12 13 22 23 {B"} = 21 {B"} cosy -siny 0 0 cos y 0 ¹j 0 sin y cos B 0 - cosa cos ß sin y-sin a cos y - sin a cos ß sin y + cos a cos y sin 3 sin y cosa sin sin a sin ß cos B
Calculate the rotation matrix, R, if frames {A} and {B} are originally coincident then (a) Frame {B} is rotated about X by 30 degrees, then about Y, by 15 degrees, and, finally, about Z by 70 degrees. (b) Frame {B} is rotated about Z, by 70 degrees, then about Y, by 15 degrees, and, finally, about Y by 70 degrees..
Transcribed Image Text:Calculate the rotation matrix, R, if frames {A} and {B} are originally coincident then (a) Frame {B} is rotated about X by 30 degrees, then about Y, by 15 degrees, and, finally, about Z by 70 degrees. (b) Frame {B} is rotated about Z, by 70 degrees, then about Y, by 15 degrees, and, finally, about Y by 70 degrees..
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