《THREE DIMENSIONAL DYNAMICS》求取 ⇩

Ⅰ．VECTOR ALGEBRA1

1．Definition and representation1

2．Addition and subtraction of vectors2

3．Multiplication of a vector by a scalar3

4．Components of a vector4

5．Linearly independent vectors5

6．Products of two vectors6

7．Products of three vectors13

8．Scalar and vector products of two vector products15

9．Division of vectors16

10．Differentiation of a vector with respect to a scalar17

11．Integration of a vector function21

12．Moment of a vector22

13．Equations of a line and a plane24

Ⅱ．MOTION OF A PARTICLE27

1．Equations of motion27

2．Components of velocity and acceleration in (ⅰ) cylindrical coordinates (ⅱ) spherical polar coordinates31

3．Motion of a heavy particle on a smooth surface of revolution33

4．Motion of a heavy particle on a smooth right circular cone46

5．Motion of a charged particle48

Ⅲ．KINEMATICAL MOTION OF A RIGID BODY54

1．Finite displacements54

2．Infinitesimal displacements58

3．Instantaneous motion of a rigid body62

Ⅳ．THEORY OF ROTATING AXES77

1．Rate of change of displacement referred to rotating axes;expression for acceleration77

2．Application to particle kinetics82

3．Motion relative to the earth89

Ⅴ．MOMENTS OF INERTIA101

1．Definition of moments and of products of inertia101

2．Radius of gyration103

3．Moment of inertia with respect to a variable line107

4．The momental ellipsoid or ellipsoid of inertia108

5．Central ellipsoid110

6．Ellipsoid of gyration111

Ⅵ．EQUATIONS OF MOTION OF A RIGID BODY120

1．Equations of motion of a system of particles．Principles of linear and angular momentum120

2．Motion of a rigid body128

Ⅶ．EULER＇S EQUATIONS AND APPLICATIONS158

1．Equations of motion referred to rotating axes158

2．Euler＇s geometrical equations164

3．Motion referred to rotating axes only one of which is fixed in the body167

4．Motion under no forces172

5．Vector treatment of the motion of a uniaxal body186

Ⅷ．PRECESSIONAL MOTION197

1．General properties197

2．Top spinning on a rough plane202

3．Top spinning on a smooth horizontal plane224

Ⅸ．IMPULSIVE MOTION229

1．Equations of impulsive motion of a particle229

2．Extension to a system of interacting particles231

3．Application to a rigid body233

4．A body is in motion when a line in the body is suddenly fixed．To find the new angular velocity of rotation238

5．General theorems243

APPENDIX:THREE DIMENSIONAL STATICS260

1．Conditions of equilibrium of a rigid body260

2．Equivalence of two sets of forces266

3．Reduction of a system of forces to a wrench266

4．Work done by a wrench269

HISTORICAL NOTE272

BIBLIOGRAPHY273

INDEX275