THREE DIMENSIONAL DYNAMICSPDF电子书下载

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Ⅰ．VECTOR ALGEBRA 1

1．Definition and representation 1

2．Addition and subtraction of vectors 2

3．Multiplication of a vector by a scalar 3

4．Components of a vector 4

5．Linearly independent vectors 5

6．Products of two vectors 6

7．Products of three vectors 13

8．Scalar and vector products of two vector products 15

9．Division of vectors 16

10．Differentiation of a vector with respect to a scalar 17

11．Integration of a vector function 21

12．Moment of a vector 22

13．Equations of a line and a plane 24

Ⅱ．MOTION OF A PARTICLE 27

1．Equations of motion 27

2．Components of velocity and acceleration in (ⅰ) cylindrical coordinates (ⅱ) spherical polar coordinates 31

3．Motion of a heavy particle on a smooth surface of revolution 33

4．Motion of a heavy particle on a smooth right circular cone 46

5．Motion of a charged particle 48

Ⅲ．KINEMATICAL MOTION OF A RIGID BODY 54

1．Finite displacements 54

2．Infinitesimal displacements 58

3．Instantaneous motion of a rigid body 62

Ⅳ．THEORY OF ROTATING AXES 77

1．Rate of change of displacement referred to rotating axes;expression for acceleration 77

2．Application to particle kinetics 82

3．Motion relative to the earth 89

Ⅴ．MOMENTS OF INERTIA 101

1．Definition of moments and of products of inertia 101

2．Radius of gyration 103

3．Moment of inertia with respect to a variable line 107

4．The momental ellipsoid or ellipsoid of inertia 108

5．Central ellipsoid 110

6．Ellipsoid of gyration 111

Ⅵ．EQUATIONS OF MOTION OF A RIGID BODY 120

1．Equations of motion of a system of particles．Principles of linear and angular momentum 120

2．Motion of a rigid body 128

Ⅶ．EULER＇S EQUATIONS AND APPLICATIONS 158

1．Equations of motion referred to rotating axes 158

2．Euler＇s geometrical equations 164

3．Motion referred to rotating axes only one of which is fixed in the body 167

4．Motion under no forces 172

5．Vector treatment of the motion of a uniaxal body 186

Ⅷ．PRECESSIONAL MOTION 197

1．General properties 197

2．Top spinning on a rough plane 202

3．Top spinning on a smooth horizontal plane 224

Ⅸ．IMPULSIVE MOTION 229

1．Equations of impulsive motion of a particle 229

2．Extension to a system of interacting particles 231

3．Application to a rigid body 233

4．A body is in motion when a line in the body is suddenly fixed．To find the new angular velocity of rotation 238

5．General theorems 243

APPENDIX:THREE DIMENSIONAL STATICS 260

1．Conditions of equilibrium of a rigid body 260

2．Equivalence of two sets of forces 266

3．Reduction of a system of forces to a wrench 266

4．Work done by a wrench 269

HISTORICAL NOTE 272

BIBLIOGRAPHY 273

INDEX 275

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