# Solucionario jerry marion

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• Publicado : 7 de julio de 2010

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CHAPTER

0

Contents

Preface

v vii

Problems Solved in Student Solutions Manual

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Matrices, Vectors, and Vector Calculus Newtonian Mechanics—Single Particle Oscillations 79 127

1 29

Nonlinear Oscillations and Chaos Gravitation 149

Some Methods in The Calculus of Variations

165 181

Hamilton’s Principle—Lagrangian and HamiltonianDynamics Central-Force Motion 233 277 333

Dynamics of a System of Particles

Motion in a Noninertial Reference Frame Dynamics of Rigid Bodies Coupled Oscillations 397 435 461 353

Continuous Systems; Waves Special Theory of Relativity

iii

iv

CONTENTS

CHAPTER

0

Preface

v vi

PREFACE

CHAPTER

1

Matrices, Vectors, and Vector Calculus

1-1.
x2 = x2′ x1′ 45˚ x1
45˚

x3

x3′

Axes x′ and x′ lie in the x1 x3 plane. 1 3 The transformation equations are:

x1 = x1 cos 45° − x3 cos 45° ′ x2 = x2 ′ x3 = x3 cos 45° + x1 cos 45° ′ x1 = ′
1 1 x1 − x3 2 2

x2 = x2 ′ x3 = ′
So the transformation matrix is: 1 1 x1 − x3 2 2

      

1 2 0 1 20 − 1 0

1  2  0  1   2 

1

2 1-2. a)
x3

CHAPTER 1

D
E

γ O α A x1

β B C

x2

From this diagram, we have

OE cos α = OA OE cos β = OB OE cos γ = OD Taking the square of each equation in (1) and adding, we find OE cos 2 α + cos 2 β + cos 2 γ  = OA + OB + OD   But
OA + OB = OC
2 2 2

(1)

2

2

2

2

(2)

(3)

and
OC + OD = OE
2 2 2...