SOLUTION MANUAL FOR Orbital Mechanics for Engineering Students 4th Edition by Howard D. Curtis ISBN: 978-0128240250 COMPLETE GUIDE ALL CHAPTERS COVERED 100% VERIFIED A+ GRADE ASSURED!!!!!NEW LATEST UPDATE!!!!!

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, SOLUTIONS MANUAL cn




to accompany
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ORBITAL MECHANICS FOR ENGINEERING STUDENTS
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Howard D. Curtis
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Embry-
Riddle Aeronautical University Daytona Be
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ach, Florida
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, Solutions Manual c n Orbital Mechanics for Engineering Student cn cn cn cn Chapter 1 cn



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Problem 1.1 cn


(a)
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
A  A  Axiˆ  Ayˆj  Azkˆ  Axiˆ  Ayˆj  Azkˆ cn
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
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
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
 Axiˆ  Axiˆ  Ayˆj  Azkˆ  Ayˆj  Axiˆ  Ayˆj  Azkˆ  Azkˆ  Axiˆ  Ayˆj  Azkˆ
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 Ax2 iˆ  iˆ Ax Ay iˆ  ˆj  Ax Az iˆ kˆ   Ay Ax ˆj  iˆ  Ay2 ˆj  ˆj  Ay Az ˆj  kˆ         
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   
  2  ˆ ˆ 
 
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 ˆ ˆcn
ˆ ˆ
 AzAx k i  AzAy k  j  Az k k cn
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 
 Ax2 1 Ax Ay 0 Ax Az 0  Ay Ax 0 Ay2 1 Ay Az 0  Az Ax 0 AzAy 0 Az2 1
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   
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
 Ax2  Ay2  Az2
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
But, according to the Pythagorean Theorem, Ax 2  yA 2 z A 2  A2 , where A  A , the magnitude of
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2
the vector A . Thus A  A  A .
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(b)
iˆ ˆj kˆ
A B  C  A  Bx
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Cx Cy Cz
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 Axiˆ  Ayˆj  Azkˆ  iˆ ByCz  BzCy  ˆjBxCz  BzCx  kˆ BxCy  ByCx 

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
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 cn
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 Ax ByCz  BzCy  Ay BxCz  BzCx  Az BxCy  ByCx cn
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or

A  B  C  AxByCz  AyBzCx  AzBxCy  AxBzCy  AyBxCz  AzByCx
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(1) c




Note that A  B  C  C  A  B , and according to (1)
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C  A  B  CxAyBz  Cy AzBx  Cz AxBy  CxAzBy  Cy AxBz  Cz AyBx
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(2) c




The right hand sides of (1) and (2) are identical. Hence A   B  C  A  B  C .
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(c)
iˆ ˆj kˆ iˆ ˆj kˆ
A  B  C Axiˆ  Ayˆj  Azkˆ  Bx
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c n By Bz c n
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Cx Cy  Cz  BzCy cn
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Cz

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
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 Ay BxCy  ByCx  Az BzCx  BxCz  iˆ  Az ByCz  BzCy  Ax BxCy  ByCx  ˆj

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 A B C  B C  A B C  B C kˆ
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 cn
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 AyBxCy  AzBxCz  AyByCx  AzBzCx iˆ  AxByCx  AzByCz  AxBxCy  AzBzCy ˆj cn  cn
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 x z x y z y x x z y y z
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 Bx AyCy  AzCz  Cx AyBy  AzBz  iˆ  By AxCx  AzCz  Cy AxBx  AzBz  ˆj
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 
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 
z x x y y z x x y y
 B A C  A C  C A B  A B  kˆ cn cn cn cn


 
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1

, Solutions Manual
c n Orbital Mechanics for Engineering Student
cn cn cn cn Chapter 1
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Add and subtract the underlined terms to get
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2