PH Stiff Body Mechanics Essay

William W. Heard

Stiff Body Mechanics

William B. Heard

Rigid Body Mechanics

Mathematics, Physics and Applications

WILEY-VCH Verlag GmbH & Co. KGaA

The Author

William B. Noticed

Alexandria, VA

USA

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ISBN-13: 978-3-527-40620-3

ISBN-10: 3-527-40620-4

This book is definitely dedicated to

Peggy

and the memory space of my

Mother and Father

VII

Contents

Preamble

XI

1

1

Shifts

1 . one particular

1 . 1 . 1

1 . 1 . two

1 . 1 ) 3

1 ) 1 . 5

1 . 1 . 5

1 ) 1 . 6th

1 . 2

1 . installment payments on your 1

1 ) 2 . a couple of

1 . installment payments on your 3

1 ) 2 . 5

1 . installment payments on your 5

1 . 3

1 ) 3. 1

1 . several. 2

1 . 4

1 ) 5

Rotations as Linear Operators one particular

Vector Algebra 1

Rotation Operators in R3 six

Rotations Particular by Axis and Perspective 8

The Cayley Change 12

Reflections 13

Euler Angles 12-15

Quaternions 17

Quaternion Algebra 20

Quaternions as Scalar–Vector Pairs twenty-one

Quaternions because Matrices 21 years old

Rotations by way of Unit Quaternions 23

Composition of Rotations 25

Sophisticated Numbers twenty nine

Cayley–Klein Guidelines 30

Rotations and the Complicated Plane thirty-one

Summary thirty five

Exercises 37

39

a couple of

Kinematics, Energy, and Energy

2 . you

2 . 1 ) 1

2 . 1 . 2

Rigid Physique Transformation forty

A Stiff Body has 6 Degrees of Freedom forty five

Any Stiff Body Change is Composed of Translation and Rotation 40

The Rotation is definitely Independent of the Reference 41

installment payments on your 1 . several

Rigid Physique Mechanics: Math, Physics and Applications. Bill B. Observed Copyright В© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-40620-4

VIII

Material

2 . 1 . 4

2 . 1 . a few

2 . a couple of

2 . 2 . 1

installment payments on your 2 . a couple of

2 . 2 . 3

installment payments on your 3

installment payments on your 4

2 . 5

2 . 6

Rigid Body Conversions Form the Group SE(3)

Chasles' Theorem forty two

Angular Velocity 44

Slanted Velocity in Euler Sides 47

Slanted Velocity in Quaternions forty-nine

Angular Speed in Cayley–Klein Parameters 60

The Masse Tensor 50

Angular Impetus 54

Kinetic Energy 54

Exercises 57

59

a few

Dynamics

a few. 1

three or more. 1 . 1

3. 1 . 2

three or more. 2

a few. 2 . you

3. 2 . 2

three or more. 2 . three or more

3. several

3. 3. 1

3. 3. two

3. several. 3

several. 4

Vectorial Mechanics sixty one

Translational and Rotational Action 61

Generalized Euler Equations 62

Lagrangian Mechanics sixty-eight

Variational Methods 68

Organic Systems and Connections 72

PoincarГ©'s Equations 75

Hamiltonian Mechanics 84

Momenta Conjugate to Euler Angles 86

Andoyer Variables 88

Conference 92

Physical exercises 98

99

4

Limited Systems

four. 1

5. 2

5. 2 . one particular

4. 2 . 2

four. 2 . 3

4. three or more

4. several. 1

some. 3. two

4. 3. 3

5. 3. some

4. four

4. 4. 1

four. 4. two

4. your five

4. 6th

Constraints 99

Lagrange Multipliers 102

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