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
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1296c196-158c-4a2c-9587-82b5996e9fed%2F88f97289-8da9-4a78-99ed-3340130956d3%2Fkhn01w8_processed.png&w=3840&q=75)
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..](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1296c196-158c-4a2c-9587-82b5996e9fed%2F88f97289-8da9-4a78-99ed-3340130956d3%2F9aerhnh_processed.png&w=3840&q=75)
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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