《ADVANCED DYNAMICS VOLⅠ》求取 ⇩

CHAPTER Ⅰ:INTRODUCTORY1

1．Introductory1

2．Position;Frames of reference1

3．Dis-placement3

4．Translation3

5．Composition of displacements3

6．Rest and motion5

7．Units5

8．Velocity5

EXERCISES Ⅰ10

9．Components of velocity of a point moving in any plane path12

EXERCISES Ⅱ15

10．Acceleration18

11．The parallelogram of accelerations21

12．Units and dimensions22

13．Acceleration of a point moving in a circle with uniform speed．Component accelerations22

EXERCISES Ⅲ25

14．Summary28

EXERCISES Ⅳ30

15．The Hodograph33

EXERCISES Ⅴ34

16．Vectors35

17．Moment of a localised vector40

18．Angular velocity and acceleration49

19．Rotation51

20．Units and dimen-sions of angular velocity and acceleration51

21．Uniform angular velocity and acceleration．Kinematic equations52

22．Examples of angular motion53

EXERCISES ⅥA55

23．Moving axes in two dimensions58

EXERCISES ⅥB61

24．Historical notes:(1)Galileo,(2)Copernicus64

CHAPTER Ⅱ:FUNDAMENTAL DYNAMICAL PRINCIPLES67

1．Newton’s Laws of Motion67

2．Evidence of their truth67

3．Ex-planation of terms used68

4．Force defined68

5．Law Ⅱ—explanation of terms used69

6．The Third Law of Motion74

7．The fundamental equation of motion76

8．The equations of motion of a particle of given mass in two dimensions77

9．Centroids of a system of mass particles79

10．Centroid considered vectorially81

11．Work82

12．Power defined88

13．Energy89

14．Equations of motion of a system of mass particles in two dimensions95

15．Sys-tem of mass particles acted on by given impulsive forces101

EXERCISES ⅦA103

EXERCISES ⅦB115

CHAPTER Ⅲ:RECTILINEAR MOTION OF A PARTICLE120

1．Expressions for velocity and acceleration120

2．Uniform accel-eration in a straight line121

3．Acceleration directed towards a fixed point in the line and varying directly as its distance from it123

4．Composition of Simple Harmonic Motions in the same straight line127

EXERCISES ⅧA129

EXERCISES ⅧB134

6．Acceleration directed away from a fixed point varying as the distance139

7．Acceleration directed to a fixed point and varying inversely as the square of the distance140

8．Motion of two bodies directly towards one another under their mutual attraction142

9．Other cases in which the acceleration is a function of the distance146

10．Agent working at constant power146

EXERCISES Ⅸ147

EXERCISES ON RESISTED MOTION150

11．Oscillating particle with superposed forced vibration153

12．Damped simple harmonic motion155

13．Resistance varying as the square of the velocity157

14．Motion under constant force subject to a resistance varying as the velocity159

EXERCISES Ⅹ162

15．Impulsive forces and impact of smooth homogeneous spheres165

EXERCISES Ⅺ168

15．6．Kinetic energy lost by impact171

EXERCISES ⅫA174

16．Rectilinear motion of a body of changing mass180

EXERCISES ⅫB181

17．Rectilinear motion of a chain183

EXERCISES ⅩⅢ188

EXERCISES ⅩⅣ192

CHAPTER Ⅳ:ACCELERATIONS PARALLEL TO RECTANGULAR AXES195

1．Equations of motion195

EXERCISES ⅩⅤ198

EXERCISES ⅩⅥ206

EXERCISES ⅩⅦ．On projectiles involving impact209

2．Motion under a force to a fixed point varying as the distance212

EXERCISES ⅩⅧ．On orbital motion under the law of direct distance215

4．Motion under the law of direct distance can be regarded as compounded of two simple harmonic motions of the same period in different directions218

5．Path when the force is repulsive218

6．Composition of simple harmonic motions in two directions219

7．Given the law of force,to find its path,and vice versa220

EXERCISES ⅩⅨ225

8．Moving axes in two dimensions227

EXERCISES ⅩⅩ231

CHAPTER Ⅴ:RADIAL AND TRANSVERSAL ACCELERATIONS—CENTRAL FORCES233

EXERCISES ⅩⅪ233

2．Forces to fixed centres,such that their magnitudes are single-valued functions of the distances from these centres,form a con-secutive system of forces239

3．Path of a particle moving under the action of a force to a fixed centre239

EXERCISES ⅩⅫ251

4．Apses and apsidal distances253

EXERCISES ⅩⅩⅢ254

EXERCISES ⅩⅩⅣ257

5．Nearly circular orbit．Condition of stability260

EXERCISES ⅩⅩⅤ262

EXERCISES ⅩⅩⅥ．Classification of orbits264

7．Equations of motion when the force is not wholly radial,the motion being in one plane269

8．Motion in a field of force in two dimensions270

9．More than one centre of force273

EXERCISES ⅩⅩⅦ274

10．Historical note explaining Newton’s methods276

CHAPTER Ⅵ:FREE MOTION UNDER THE LAW OF INVERSE SQUARE280

1．Law of force to the focus of a conic is that of the inverse square of the distance280

2．Particle projected with velocity V from a point P,under a force μ/r2 per unit mass directed towards a fixed point S,where SP=r will describe a conic having S as focus281

3．Periodic time of orbit282

4．Construction of orbit282

5．Hodo-graph of orbit284

EXERCISES ⅩⅩⅧ289

6．Envelope of trajectories with given speed of projection291

7．Two possible directions with given speed at P to pass through Q292

8．Projection from the Earth taking account of variations of gravity293

EXERCISES ⅩⅩⅨ293

9．Time of describing any part of the orbit296

10．Kepler’s laws302

11．Newton’s Law of Gravitation303

12．The corrected form of Kepler’s laws304

EXERCISES ⅩⅩⅩ306

13．Perturbations308

EXERCISES ⅩⅩⅪ309

14．Historical Notes:(1)Newton,(2)Kepler314

CHAPTER Ⅶ:CONSTRAINED MOTION IN TWO DIMENSIONS319

1．One-sided constraints319

2．Smooth fixed curve319

EXERCISES ⅩⅩⅫ321

3．Time of describing an arc324

EXERCISES ⅩⅩⅩⅢ328

4．Principles of conservation of energy and conservation of linear and angular momentum applied to cases of motion of connected particles330

5．Small oscillations about a position of equilibrium of a system having one degree of freedom334

EXERCISES ⅩⅩⅩⅣ335

6．Motion of a particle at the end of a fine inextensible string wound on a fixed plane curve338

7．Motion of a particle in a smooth tube in form of a plane curve,rotating in its own plane about a fixed point339

EXERCISES ⅩⅩⅩⅤ341

8．Motion of a particle sliding on a rough plane curve in a vertical plane346

EXERCISES ⅩⅩⅩⅥ348

CHAPTER Ⅷ:MOTION IN A RESISTING MEDIUM351

1．Complete solution in general impossible351

EXERCISES ⅩⅩⅩⅦ352

2．Motion of a heavy particle in a medium in which the resistance varies as the square of the velocity354

3．Systematic method by Greenhill355

EXERCISES ⅩⅩⅩⅧ357

4．The instantaneous parabola359

5．Motion in a resisting medium under a central force360

EXERCISES ⅩⅩⅩⅨ361

CHAPTER Ⅸ:MOTION OF A CHAIN IN TWO DIMENSIONS363

1．Equations of motion363

EXERCISES ⅩL364

2．Initial motion of a chain365

EXERCISES ⅩLⅠ367

EXERCISES ⅩLⅡ368

3．Motion of a chain under impulses369

EXERCISES ⅩLⅢ370

4．Motion of a chain inside a smooth tube in the form of a plane curve372

EXERCISES ⅩLⅣ373

5．Case of a Chain in a rotating tube375

EXERCISES ⅩLⅤ377

CHAPTER Ⅹ:MOTION OF A PARTICLE IN THREE DIMENSIONS378

1．Component accelerations in Cartesian,spherical polar and cylindrical coordinates378

2．Motion of a heavy particle on a smooth fixed surface of revolution whose axis is vertical379

EXERCISES ⅩLⅥ383

3．The spherical pendulum384

EXERCISES ⅩLⅦ385

4．Motion on the surface of a right circular cone389

EXERCISES ⅩLⅧ389

EXERCISES ⅩLⅨ392

5．Component accelerations of a point moving in a tortuous curve395

6．Motion of a particle on a fixed surface397

7．Motion of a bead on a smooth wire,in the form of a plane curve,which is made to rotate with constant angular velocity about a fixed vertical axis in its plane400

EXERCISES L401

8．Motion of a heavy chain in a smooth tube in the form of a plane curve which is made to revolve uniformly about a vertical axis in its plane404

EXERCISES LⅠ405

9．Vectorial character of angular velocity406

10．Instantaneous axis when one point fixed in rigid body407

11．The parallelepiped of velocities,linear and angular407

12．Velocities and accelerations of a point referred to three moving axes mutually at right angles407

13．Motion of a particle near the Earth’s surface,taking into account the Earth’s rotation410

EXERCISES LⅡ413

INDEX417