Instructor’s Solutions Manual To Accompany Analytical Mechanics 7th Edition

,Instructor’s Solutions Manual
To Accompany


Analytical Mechanics
7th Edition

Grant R. Fowles - University of Utah
George L. Cassiday - University of Utah




ISBN-10: 0-534-49493-5
ISBN-13: 978-0-534-49493-3

, Contents


1. Fundamental Concepts: Vectors.
2. Newtonian Mechanics: Rectilinear Motion of a Particle.
3. Oscillations.
4. General Motion of a Particle in Three Dimensions.
5. Noninertial Reference Systems.
6. Gravitation and Central Forces.
7. Dynamics of Systems of Particles.
8. Mechanics of Rigid Bodies: Planar Motion.
9. Motion of Rigid Bodies in Three Dimensions.
10. Lagrangian Mechanics.
11. Dynamics of Oscillating Systems.

, CHAPTER 1
FUNDAMENTAL CONCEPTS: VECTORS

K K
1.1 (a) A + B = (iˆ + ˆj) + ( j + kˆ) = i + 2 j + kˆˆ
ˆ ˆ
K K 1

A + B = (1+ 4 +1)2 = 6
K K
ˆ ˆ ˆ ˆ ˆ ˆ ˆ
(b) 3A − 2B = 3(i + j) − 2( j + k ) = 3i + j − 2k
K K
(c) A  B = (1)(0) + (1)(1) + (0)(1) = 1


K iˆ ˆj kˆ
(d) K  = 1 ˆ ˆ ˆ ˆ
ˆ
B 1 ˆj
A 0 1 1 0 = i (1− 0) + j(0 −1) + k (1− 0) = i − +k


K K 1
A B = (1+1 +1) 2 = 3

K K K
( )( )
1.2 (a) A  ( B + C ) = 2iˆ + ˆj  i + 4 j + ˆkˆ = (2)(1) + (1)(4) + (0)(1) = 6
ˆ
K K K ˆ ˆ ˆ ˆ
( A + B) C = (3i + j + k ) 4 j = (3)(0) + (1)(4) + (1)(0) = 4
K K K 2 1 0

(b) A  ( B  C ) = 1 0 1 = −8
0 4 0
K K K K K K
( A B )  C = A  ( B  C ) = −8
K K K K K K K K K ˆ ˆ ˆ ˆ
ˆ ˆ
( ) ( )
(c) A ( B  C ) = ( A  C ) B − ( A  B ) C = 4 i + k − 2 4 j = 4i − 8 j + 4k
K K K K K K K K K K K K
 
( A B )  C = −C  ( A B) = − (C  B) A − (C  A) B
( ) ( )
= − 0 2iˆ + ˆj − 4 iˆ + kˆ  = 4iˆ + 4kˆ




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