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
Related questions
Question
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.

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

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..
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 6 steps with 20 images

Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you

Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press

Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON

Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education

Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press

Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON

Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education

Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY

Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning

Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY