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John Taylor has brought to his new book, Classical Mechanics, all of the clarity and insight that made his introduction to Error Analysis a best-selling text. Classical Mechanics is intended for students who have studied some mechanics in an introductory physics course and covers such topics as conservation laws, oscillations, Lagrangian mechanics, two-body problems, non-inertial frames, rigid bodies, normal modes, chaos theory, Hamiltonian mechanics, and continuum mechanics. A particular highlight is the chapter on chaos, which focuses on a few simple systems, to give a truly comprehensible introduction to the concepts that we hear so much about. At the end of each chapter is a large selection of interesting problems for the student, classified by topic and approximate difficulty, and ranging from simple exercises to challenging computer projects. Taylor's Classical Mechanics is a thorough and very readable introduction to a subject that is four hundred years old but as exciting today as ever. He manages to convey that excitement as well as deep understanding and insight. Contents; 6 Preface; 12 Part 1 Essentials; 16 1 Newton's Laws of Motion; 18 1.1 Classical Mechanics; 18 1.2 Space and Time; 19 1.3 Mass and Force; 24 1.4 Newton's 1st and 2nd Laws; 28 1.5 The 3rd Law and Conservation of Momentum; 32 1.6 Newton's 2nd Law in Cartesian Coordinates; 38 1.7 2D Polar Coordinates; 41 Problems for Chapter 1; 49 2 Projectiels and Charged Particels; 58 2.1 Air Resistance; 58 2.2 Linear Air Resistance; 61 2.3 Trajectory and Range in a Linear Medium; 69 2.4 Quadratic Air Resistance; 72 2.5 Motion of a Charge in a Uniform Magnetic Field; 80 2.6 Complex Exponentials; 83 2.7 Solution for the Charge in a B Field; 85 Problems for Chapter 2; 87 3 Momentum and Angular Momentum; 98 3.1 Conservation of Momentum; 98 3.2 Rockets; 100 3.3 The Center of Mass; 102 3.4 Angular Momentum for a Single Particle; 105 3.5 Angular Momentum for Several Particles; 108 Problems for Chapter 3; 114 4 Energy; 120 4.1 Kinetic Energy and Work; 120 4.2 Potential Energy and Conservative Forces; 124 4.3 Force as the Gradient of Potential Energy; 131 4.4 The Second Condition that F be Conservative; 133 4.5 Time-Dependent Potential Energy; 136 4.6 Energy for Linear 1D systems; 138 4.7 Curvilinear 1D Systems; 144 4.8 Central Forces; 148 4.9 Energy of Interaction of 2 Particles; 153 4.10 The Energy of a Multiparticle System; 159 Problems for Chapter 4; 165 5 Oscillations; 176 5.1 Hooke's Law; 176 5.2 Simple Harmonic Motion; 178 5.3 2D Oscillators; 185 5.4 Damped Oscillations; 188 5.5 Driven Damped Oscillations; 194 5.6 Resonance; 202 5.7 Fourier Series; 207 5.8 Fourier Series for the Driven Oscillator; 212 5.9 The RMS Displacement\; Parseval's Theorem; 218 Problems for Chapter 5; 222 6 Calculus of Variations; 230 6.1 Two Examples; 231 6.2 The Euler-Lagrange Equation; 233 6.3 Applications of the Euler-Lagrange Equation; 236 6.4 More than Two Variables; 241 Problems for Chapter 6; 245 7 Lagrange's Equations; 252 7.1 Lagrange's Equations for Unconstrained Motion; 253 7.2 Constrained Systems\; an Example; 260 7.3 Constrained Systems in General; 262 7.4 Proof of Lagrange's Equations with Constraints; 265 7.5 Examples of Lagrange's Equations; 269 7.6 Generalized Momenta and Ignorable Coordinates; 281 7.7 Conclusion; 282 7.8 More about Conservation Laws; 283 7.9 Lagrange's Equations for Magnetic Forces; 287 7.10 Lagrange Multipliers and Constraint Forces; 290 Problems for Chapter 7; 296 8 Two-Body Central-Force Problems; 308 8.1 The Problem; 308 8.2 CM and Relative Coordinates\; Reduced Mass; 310 8.3 The Equations of Motion ; 312 8.4 The Equivalent 1D Problem; 315 8.5 The Equation of the Orbit; 320 8.6 The Kelper Orbits; 323 8.7 The Unbounded Kelper Orbits; 328 8.8 Changes of Orbit; 330 Problems for Chapter 8; 335 9 Mechanics in Noninertial Frames; 342 9.1 Acceleration without Rotation; 342 9.2 The Tides; 345 9.3 The Angular Velocity Vector; 351 9.4 Time Derivatives in a Rotating Frame; 354 9.5 Newton's 2nd Law in a Rotating Frame ; 357 9.6 The Centrifugal Force; 359 9.7 The Coriolis Force; 363 9.8 Free Fall and the Coriolis Force; 366 9.9 The Foucault Pendulum; 369 9.10 Coriolis Force and Coriolis Acceleration; 373 Problems for Chapter 9; 375 10 Rotational Motion of Rigid Bodies; 382 10.1 Properties of the Center of Mass; 382 10.2 Rotation about a Fixed Axis; 387 10.3 Rotation about Any Axis\; the Inertia Tensor; 393 10.4 Principal Axes of Inertia; 402 10.5 Finding the Principal Axes\; Eigenvalue Equations; 404 10.6 Precession of a Top due to a Weak Torque; 407 10.7 Euler's Equations; 409 10.8 Euler's Equations with Zero Torque; 412 10.9 Euler Angle; 416 10.10 Motion of a Spinning Top; 418 Problems for Chapter 10; 423 11 Coupled Oscillators and Normal Modes; 432 11.1 Two Masses and Three Springs; 432 11.2 Identical Springs and Equal Masses ; 436 11.3 Two Weakly couples Oscillators; 441 11.4 Lagrangian Approach\: The Double Pendulum; 445 11.5 The General Case; 451 11.6 Three Coupled Pendulums; 456 11.7 Normal Coordinates; 459 Problems for Chapter 11; 463 Part 2 Further Topics; 470 12 Nonlinear Mechanics and Chaos; 472 12.1 Linearity and Nonlinearity; 473 12.2 The Driven Damped Pendulum; 479 12.3 Some Expected Features of the DDP; 480 12.4 The DDP\: Approach to Chaos; 484 12.5 Chaos and Sensitivity to Initial Conditions; 493 12.6 Bifurcation Diagrams; 500 12.7 State-Space Orbits; 504 12.8 Poincare' Sections; 512 12.9 The Logistic Map; 515 Problems for Chapter 12; 531 13 Hamiltonian Mechanics; 538 13.1 The Basic Variables; 539 13.2 Hamilton's Equation for 1D Systems; 541 13.3 Hamilton's Equations in Several Dimensions; 545 13.4 Ignorable Coordinates; 552 13.5 Lagrange's Equations vs Hamilton's Equations; 553 13.6 Phase-Space Orbits; 555 13.7 Liouville's Theorem; 560 Problems for Chapter 13; 567 14 Collision Theory; 574 14.1 The Scattering Angle and Impact Parameter; 575 14.2 The Collision Cross Section ; 577 14.3 Generalizations of the Cross Section; 580 14.4 The Differential Scattering Cross Section; 585 14.5 Calculating the Differential Cross Section; 589 14.6 Rutherford Scattering ; 591 14.7 Cross Sections in Various Frames; 596 14.8 Relation of the CM and Lab Scattering Angles ; 599 Problems for Chapter 14; 604 15 Special Relativity; 612 15.1 Relativity; 613 15.2 Galilean Relativity; 613 15.3 The Postulates of Special Relativity; 620 15.4 The Realativity of Time\; Time Dilation; 622 15.5 Length Contraction; 627 15.6 The Lorentz Transformation; 629 15.7 The Relativistic Velocity-Addition Formula; 634 15.8 4D Space-Time\; Four-Vectors; 636 15.9 The Invariant Scalar Product; 642 15.10 The Light Cone; 644 15.11 The Quotient Rule and Dopler Effect; 649 15.12 Mass, Four-Velocity, and Four-Momentum; 652 15.13 Energy, the Fourth Component of Momentum; 657 15.14 Collisions; 663 15.15 Force in Relativity; 668 15.16 Massless Particles\; the Photon; 671 15.17 Tensors; 675 15.18 Electrodynamics; 679 Problems for Chapter 15; 685 John Taylor has brought to his most recent book, Classical Mechanics, all of the clarity and insight that made his Introduction to Error Analysis a best-selling text. Classical Mechanics is intended for students who have studied some mechanics in an introductory physics course, such as "freshman physics." With unusual clarity, the book covers most of the topics normally found in books at this level, including conservation laws, oscillations, Lagrangian mechanics, two-body problems, non-inertial frames, rigid bodies, normal modes, chaos theory,Hamiltonian mechanics, and continuum mechanics. A particular highlight is the chapter on chaos, which focuses on a few simple systems, to give a truly comprehensible introduction to the concepts that we hear so much about. At the end of each chapter is a large selection of interesting problems for the student, 744 in all, classified by topic and approximate difficulty, and ranging from simple exercises to challenging computer projects. "Classical Mechanics is intended for students who have studied some mechanics in an introductory physics course, such as "freshman physics." ...the book covers most of the topics normally found in books at this level, including conservation laws, oscillations, Lagrangian mechanics, two-body problems, non-inertial frames, rigid bodies, normal modes, chaos theory, Hamiltonian mechanics, and continuum mechanics. A particular highlight is the chapter on chaos, which focuses on a few simple systems, to give a truly comprehensible introduction to the concepts that we hear so much about. At the end of each chapter is a large selection of interesting problems for the student, 744 in all, classified by topic and approximate difficulty, and ranging for simple exercises to challenging computer projects." -- Publisher's description. "Classical Mechanics is intended for students who have studied some mechanics in an introductory physics course, such as "freshman physics." ... the book covers most of the topics normally found in books at this level, including conservation laws, oscillations, Lagrangian mechanics, two-body problems, non-inertial frames, rigid bodies, normal modes, chaos theory, Hamiltonian mechanics, and continuum mechanics. A particular highlight is the chapter on chaos, which focuses on a few simple systems, to give a truly comprehensible introduction to the concepts that we hear so much about. At the end of each chapter is a large selection of interesting problems for the student, 744 in all, classified by topic and approximate difficulty, and ranging for simple exercises to challenging computer projects."-- Provided by publisher Classical Mechanics is intended for students who have studied some mechanics in an introductory physics course, such as “freshman physics'. With unusual clarity, the book covers most of the topics normally found in books at this level, including conservation laws, oscillations, Lagrangian mechanics, two-body problems, non-inertial frames, rigid bodies, normal modes, chaos theory, Hamiltonian mechanics, and continuum mechanics. A particular highlight is the chapter on chaos, which focuses on a few simple systems, to give a truly comprehensible introduction to the concepts that we hear so much about. At the end of each chapter is a large selection of interesting problems for the student, 744 in all, classified by topic and approximate difficulty, and ranging for simple exercises to challenging computer projects. Mechanics is the study of how things move: how planets move around the sun, how a skier moves down the slope, or how an electron moves around the nucleus of an atom.