Mechanics (3rd Edition)

this Text Is Intended As The Basis For An Intermediate Course In Mechanics At The Undergraduate Level. Such A Course, As Essential Preparation For Advanced Work In Physics, Has Several Major Objectives. It Must Develop In The Student A Thorough Understanding Of The Fundamental Principles Of Mechanics. It Should Treat In Detail Certain Specific Problems Of Primary Importance In Physics, For Example, The Harmonic Oscillator And The Motion Of A Particle Under A Central Force. Cover......Page 1 Mechanics......Page 4 Copyright......Page 5 Preface......Page 6 Contents......Page 10 1.1 Mechanics, an exact science......Page 16 1.2 Kinematics, the description of motion......Page 18 1.3 Dynamics. Mass and force......Page 20 1.4 Newton's laws of motion......Page 22 1.5 Gravitation......Page 25 1.6 Units and dimensions......Page 26 1.7 Some elementary problems in mechanics......Page 27 2.1 Momentum and energy theorems......Page 36 2.2 Discussion of the general problem of one-dimensional motion......Page 37 2.3 Applied force depending on the time......Page 39 2.4 Damping force depending on the velocity......Page 42 2.5 Conservative force depending on position Potential energy......Page 45 2.6 Falling bodies......Page 50 2.7 The simple harmonic oscillator......Page 54 2.8 Linear differential equations with constant coefficients......Page 56 2.9 The damped harmonic oscillator......Page 61 2.10 The forced harmonic oscillator......Page 65 2.11 The principle of superposition. Harmonic oscillator with arbitrary applied force.......Page 73 3.1 Vector algebra......Page 87 3.2 Applications to a set of forces acting on a particle......Page 96 3.3 Differentiation and integration of vectors......Page 100 3.4 Kinematics in a plane......Page 106 3.5 Kinematics in three dimensions......Page 109 3.6 Elements of vector analysis......Page 113 3.7 Momentum and energy theorems......Page 118 3.8 Plane and vector angular momentum theorems......Page 120 3.9 Discussion of the general problem of two- and three-dimensional motion......Page 122 3.10 The harmonic oscillator in two and three dimensions......Page 124 3.11 Projectiles......Page 126 3.12 Potential energy......Page 130 3.13 Motion under a central force......Page 137 3.14 The central force inversely proportional to the square of the distance......Page 143 3.15 Elliptic orbits. The Kepler problem.......Page 150 3.16 Hyperbolic orbits. The Rutherford problem. Scattering cross section.......Page 152 3.17 Motion of a particle in an electromagnetic field......Page 155 4.1 Conservation of linear momentum. Center of mass......Page 175 4.2 Conservation of angular momentum......Page 178 4.3 Conservation of energy......Page 181 4.4 Critique of the conservation laws......Page 184 4.5 Rockets, conveyor belts, and planets......Page 187 4.6 Collision problems......Page 190 4.7 The two-body problem......Page 197 4.8 Center-of-mass coordinates. Rutherford scattering by a charged particle of finite mass.......Page 200 4.9 The N-body problem......Page 203 4.10 Two coupled harmonic oscillators......Page 206 5.1 The dynamical problem of the motion of a rigid body......Page 222 5.2 Rotation about an axis......Page 225 5.3 The simple pendulum......Page 227 5.4 The compound pendulum......Page 230 5.5 Computation of centers of mass and moments of inertia......Page 233 5.6 Statics of rigid bodies......Page 243 5.7 Statics of structures......Page 248 5.8 Stress and strain......Page 250 5.9 Equilibrium of flexible strings and cables......Page 252 5.10 Equilibrium of solid beams......Page 256 5.11 Equilibrium of fluids......Page 262 6.1 Centers of gravity for extended bodies......Page 274 6.2 Gravitational field and gravitational potential......Page 276 6.3 Gravitational field equations......Page 279 7.1 Moving origin of coordinates......Page 286 7.2 Rotating coordinate systems......Page 288 7.3 Laws of motion on the rotating earth......Page 295 7.4 The Foucault pendulum......Page 296 7.5 Larmor's theorem......Page 299 7.6 The restricted three-body problem......Page 301 8.1 The equation of motion for the vibrating string......Page 310 8.2 Normal modes of vibration for the vibrating string......Page 312 8.3 Wave propagation along a string......Page 316 8.4 The string as a limiting case of a system of particles......Page 320 8.5 General remarks on the propagation of waves......Page 325 8.6 Kinematics of moving fluids......Page 328 8.7 Equations of motion for an ideal fluid......Page 335 8.8 Conservation laws for fluid mqJ:ion......Page 337 8.9 Steady flow......Page 343 8.10 Sound waves......Page 346 8.11 Normal vibrations of fluid in a rectangular box......Page 350 8.12 Sound waves in pipes......Page 354 8.13 Group velocity......Page 355 8.14 The Mach number......Page 357 8.15 Viscosity......Page 360 9.1 Generalized coordinates......Page 368 9.2 Lagrange's equations......Page 378 9.3 Examples......Page 381 9.4 Systems subject to constraints......Page 383 9.5 Examples of systems subject to constraints......Page 387 9.6 Constants of the motion and ignorable coordinates......Page 393 9.7 Further examples......Page 395 9.8 Electromagnetic forces and velocity-dependent potentials......Page 400 9.9 Lagrange's equations for the vibrating string......Page 403 9.10 Hamilton's equations......Page 407 9.11 Liouville's theorem......Page 410 10.1 Angular momentum of a rigid body......Page 417 10.2 Tensor algebra......Page 418 10.3 Coordinate transformations......Page 425 10.4 Diagonalization of a symmetric tensor......Page 430 10.5 The inertia tensor......Page 439 10.6 The stress tensor......Page 446 11.1 Motion of a rigid body in space......Page 459 11.2 Euler's equations of motion for a rigid body......Page 460 11.3 Poinsot's solution for a freely rotating body......Page 464 11.4 Euler's angles......Page 466 11.5 The symmetrical top......Page 469 12.1 Condition for stability near an equilibrium configuration......Page 480 12.2 Linearized equations of motion near an equilibrium configuration......Page 482 12.3 Normal modes of vibration......Page 484 12.4 Forced vibrations, damping......Page 488 12.5 Perturbation theory......Page 490 12.6 Small vibrations about steady motion......Page 496 12.7 Betatron oscillations in an accelerator......Page 501 12.8 Stability of Lagrange's three bodies......Page 505 13.1 The postulates of the special theory of relativity......Page 517 13.2 The apparent paradox concerning the velocity of light......Page 520 13.3 Coordinate systems, frames of reference......Page 523 13.4 Behavior of clocks and meter sticks......Page 534 13.5 The Lorentz transformation......Page 538 13.6 Some applications of the Lorentz transformation......Page 542 14.1 Space-time vector algebra......Page 552 14.2 The relativistic conservation laws......Page 563 14.3 Collision theory......Page 567 14.4 The relativistic equations of motion......Page 573 14.5 Solutions of the equations of motion......Page 575 14.6 Relativistic force laws. Electrodynamics.......Page 582 14.7 Tensor algebra in the 4-dimensional space......Page 589 14.8 The general theory of relativity......Page 591 Bibliography......Page 610 Answers to Odd-Numbered Problems......Page 616 Index of Symbols......Page 630 Index......Page 642