Classical Mechanics: A Modern Introduction

by Martin W. McCall (Imperial College of Science, Technology and Medicine)

• ISBN13: 9780471497110
• ISBN10: 0471497118
• Format: Hardcover
• Copyright: 2000-12-01
• Publisher: WILEY

Summary

* Revision notes at the end of each chapter

Table of Contents

Preface	xi
Newton's Laws	1	(18)
What is Mechanics?	1	(1)
Mechanics as a Scientific Theory	1	(1)
Newtonian vs. Einsteinian Mechanics	2	(1)
Newton's Laws	3	(4)
A Deeper Look at Newton's Laws	7	(3)
Inertial Frames	10	(3)
Newton's Laws in Non-Inertial Frames	13	(1)
Switching off Gravity	14	(2)
Finale---Laws, Postulates or Definitions?	16	(1)
Summary	16	(2)
Problems	18	(1)
One-Dimensional Motion	19	(30)
Rationale for One-Dimensional Analysis	19	(2)
The Concept of a Particle	21	(1)
Motion with a Constant Force	21	(1)
Work and Energy	22	(2)
Impulse and Power	24	(1)
Motion with a Position-Dependent Force	25	(3)
The Nature of Energy	28	(2)
Potential Functions	30	(3)
Equilibria	33	(1)
Motion Close to a Stable Equilibrium	34	(1)
The Stability of the Universe	35	(5)
Motion with a Velocity-Dependent Force	40	(2)
Summary	42	(3)
Problems	45	(4)
Oscillatory Motion	49	(48)
Introduction	49	(1)
Prototype Harmonic Oscillator	50	(1)
Differential Equations	51	(1)
General Solution for Simple Harmonic Motion	52	(3)
Energy in Simple Harmonic Motion	55	(1)
Damped Oscillations	56	(5)
Light Damping--the Q Factor	61	(2)
Heavy Damping and Critical Damping	63	(3)
Forced Oscillations	66	(8)
Complex Number Method	74	(3)
Electrical Analogue	77	(2)
Power in Forced Oscillations	79	(1)
Coupled Oscillations	80	(8)
Summary	88	(2)
Problems	90	(7)
Two-Body Dynamics	97	(30)
Rationale	97	(1)
Centre of Mass	97	(2)
Internal Motion---Reduced Mass	99	(1)
Collisions	100	(3)
Elastic Collisions	103	(5)
Inelastic Collisions	108	(1)
Centre of Mass Frame	109	(6)
Rocket Motion	115	(3)
Launch Vehicles	118	(2)
Summary	120	(2)
Problems	122	(5)
Relativity 1: Space and Time	127	(36)
Why Relativity?	127	(1)
Galilean Relativity	128	(1)
The Fundamental Postulates of Relativity	129	(5)
Inertial Observers in Relativity	134	(2)
Comparing Transverse Distances Between Frames	136	(2)
Lessons from a Light Clock---Time Dilation	138	(3)
Proper Time	141	(1)
Interval Invariance	142	(2)
The Relativity of Simultaneity	144	(1)
The Relativity of Length---Length Contraction	145	(2)
The Lorentz Transformations	147	(5)
Velocity Addition	152	(2)
Particles Moving Faster Than Light---Tachyons	154	(1)
Summary	155	(3)
Problems	158	(5)
Relativity 2: Energy and Momentum	163	(26)
Energy and Momentum	163	(7)
The Meaning of Rest Energy	170	(2)
Relativistic Collisions and Decays	172	(2)
Photons	174	(3)
Units in High-Energy Physics	177	(2)
Energy/Momentum Transformations Between Frames	179	(3)
Relativistic Doppler Effect	182	(2)
Summary	184	(2)
Problems	186	(3)
Gravitational Orbits	189	(28)
Introduction	189	(1)
Work in Three Dimensions	189	(2)
Torque and Angular Momentum	191	(3)
Central Forces	194	(6)
Gravitational Orbits	200	(9)
Kepler's Laws	209	(2)
Comments	211	(1)
Summary	212	(1)
Problems	213	(4)
Rigid Body Dynamics	217	(28)
Introduction	217	(1)
Torque and Angular Momentum for Systems of particles	218	(2)
Centre of Mass of Systems of Particles and Rigid Bodies	220	(3)
Angular Momentum of Rigid Bodies	223	(7)
Kinetic Energy of Rigid Bodies	230	(1)
Bats, Cats, Pendula and Gyroscopes	231	(9)
Summary	240	(1)
Problems	241	(4)
Rotating Frames	245	(16)
Introduction	245	(1)
Experiments on Roundabouts	246	(3)
General Prescription for Rotating Frames	249	(3)
The Centrifugal Term	252	(2)
The Coriolis Term	254	(2)
Final Thoughts	256	(1)
Summary	257	(1)
Problems	258	(3)
Appendix	261	(4)
Answers to Problems	265	(4)
Bibliography	269	(2)
Index	271