Advanced Engineering Dynamics Homework Assignment: Chapter 1, Exercises of Dynamics

A homework assignment from chapter 1 of the advanced engineering dynamics textbook by ali meghdari, covering topics such as direct expansion, indicial notations method, and calculating the divergence and curl of a vector field. Students are asked to prove various equations and find the divergence and curl of a given vector field.

Typology: Exercises

2019/2020

Uploaded on 11/14/2020

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ADVANCED ENGINEERING DYNAMICS CHAPTER-1
By: Ali Meghdari Sharif University of Technology
Homework Assignment: # 1
1. By direct expansion show that:
a)
6
ijkijk
b)
0
kjijk dd
2. Use the indicial notations method to prove the followings:
a)
})(:int{,)()()( kpjqkqjpipqijk
HCBABCACBA
b)
)()()( BACACBCBA
c)
))(())(()()( CBDADBCADCBA
d)
babaababba )()()()()(
e)
VVV 2
)()(
or V
2
-) V) = Grad.(Div. VCurl(Curl
f)
0
of: Curland the Divergence3. Find the

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ADVANCED ENGINEERING DYNAMICS CHAPTER- By: Ali Meghdari Sharif University of Technology Homework Assignment: # 1

  1. By direct expansion show that:

a)  ijk^  ijk ^6

b)^  ijk djdk ^0

  1. Use the indicial notations method to prove the followings: a) A ( BC )( AC ) B ( AB ) C , { H int:  (^) ijkipq ( jpkq  jqkp ) } b) A ( BC ) B ( CA ) C ( AB ) c) ( AB )( CD )( AC )( BD )( AD )( BC ) d) ( ab )( b ) ab ( a ) a ( b )( a ) b e) V or (  V )( V )^2 V 2 Curl(CurlV) = Grad.(Div.V)-  f)  0
  2. Find theDivergenceand theCurl of: 1 2 3 2 1 3 2 3 2 2 3 1 2 2 F ( x 1  x x ) e ( xxx ) e ( xxx ) e