Classical Mechanics

NOTE EDITORE

Classical Mechanics, Second Edition presents a complete account of the classical mechanics of particles and systems for physics students at the advanced undergraduate level. The book evolved from a set of lecture notes for a course on the subject taught by the author at California State University, Stanislaus, for many years. It assumes the reader has been exposed to a course in calculus and a calculus-based general physics course. However, no prior knowledge of differential equations is required. Differential equations and new mathematical methods are developed in the text as the occasion demands.The book begins by describing fundamental concepts, such as velocity and acceleration, upon which subsequent chapters build. The second edition has been updated with two new sections added to the chapter on Hamiltonian formulations, and the chapter on collisions and scattering has been rewritten. The book also contains three new chapters covering Newtonian gravity, the Hamilton-Jacobi theory of dynamics, and an introduction to Lagrangian and Hamiltonian formulations for continuous systems and classical fields. To help students develop more familiarity with Lagrangian and Hamiltonian formulations, these essential methods are introduced relatively early in the text. The topics discussed emphasize a modern perspective, with special note given to concepts that were instrumental in the development of modern physics, for example, the relationship between symmetries and the laws of conservation. Applications to other branches of physics are also included wherever possible. The author provides detailed mathematical manipulations, while limiting the inclusion of the more lengthy and tedious ones. Each chapter contains homework problems of varying degrees of difficulty to enhance understanding of the material in the text. This edition also contains four new appendices on D'Alembert's principle and Lagrange's equations, derivation of Hamilton’s principle, Noether’s theorem, and conic sections.

SOMMARIO

Kinematics: Describing the MotionIntroductionSpace, Time, and Coordinate SystemsChange of Coordinate System (Transformation of Components of a Vector)Displacement VectorSpeed and VelocityAccelerationVelocity and Acceleration in Polar CoordinatesAngular Velocity and Angular AccelerationInfinitesimal Rotations and the Angular Velocity VectorNewtonian MechanicsThe First Law of Motion (Law of Inertia)The Second Law of Motion; the Equations of MotionThe Third Law of MotionGalilean Transformations and Galilean InvarianceNewton’s Laws of Rotational MotionWork, Energy, and Conservation LawsSystems of ParticlesReferencesIntegration of Newton’s Equation of MotionIntroductionMotion Under Constant ForceForce Is a Function of TimeForce Is a Function of VelocityForce Is a Function of PositionTime-Varying Mass System (Rocket System)Lagrangian Formulation of Mechanics: Descriptions of Motion in Configuration SpaceGeneralized Coordinates and ConstraintsKinetic Energy in Generalized CoordinatesGeneralized MomentumLagrangian Equations of MotionNonuniqueness of the LagrangianIntegrals of Motion and Conservation LawsScale InvarianceNonconservative Systems and Generalized PotentialCharged Particle in Electromagnetic FieldForces of Constraint and Lagrange’s MultipliersLagrangian versus Newtonian Approach to Classical MechanicsReferenceHamiltonian Formulation of Mechanics: Descriptions of Motion in PhaseSpacesThe Hamiltonian of a Dynamic SystemHamilton’s Equations of MotionIntegrals of Motion and Conservation TheoremsCanonical TransformationsPoisson BracketsPoisson Brackets and Quantum MechanicsPhase Space and Liouville’s TheoremTime Reversal in Mechanics (Optional)Passage from Hamiltonian to LagrangianReferencesMotion Under a Central ForceTwo-Body Problem and Reduced MassGeneral Properties of Central Force MotionEffective Potential and Classification of OrbitsGeneral Solutions of Central Force ProblemInverse Square Law of ForceKepler’s Three Laws of Planetary MotionApplications of Central Force MotionNewton’s Law of Gravity from Kepler’s LawsStability of Circular Orbits (Optional)Apsides and Advance of Perihelion (Optional)Laplace–Runge–Lenz Vector and the Kepler Orbit (Optional)ReferencesHarmonic OscillatorSimple Harmonic OscillatorAdiabatic Invariants and Quantum ConditionDamped Harmonic OscillatorPhase Diagram for Damped OscillatorRelaxation Time PhenomenaForced Oscillations without DampingForced Oscillations with DampingOscillator Under Arbitrary Periodic ForceVibration IsolationParametric ExcitationCoupled Oscillations and Normal CoordinatesCoupled PendulumCoupled Oscillators and Normal Modes: General Analytic ApproachForced Oscillations of Coupled OscillatorsCoupled Electric CircuitsNonlinear OscillationsQualitative Analysis: Energy and Phase DiagramsElliptical Integrals and Nonlinear OscillationsFourier Series ExpansionsThe Method of PerturbationRitz MethodMethod of Successive ApproximationMultiple Solutions and JumpsChaotic OscillationsReferencesCollisions and ScatteringsDirect Impact of Two ParticlesScattering Cross Sections and Rutherford ScatteringLaboratory and Center-of-Mass Frames of ReferenceNuclear SizesSmall-Angle Scattering (Optional)ReferencesMotion in Non-Inertial SystemsAccelerated Translational Coordinate SystemDynamics in Rotating Coordinate SystemMotion of Particle Near the Surface of the EarthFoucault PendulumLarmor’s TheoremClassical Zeeman EffectPrinciple of EquivalenceMotion of Rigid BodiesIndependent Coordinates of Rigid BodyEulerian AnglesRate of Change of VectorRotational Kinetic Energy and Angular MomentumInertia TensorEuler’s Equations of MotionMotion of a Torque-Free Symmetrical TopMotion of Heavy Symmetrical Top with One Point FixedStability of Rotational MotionReferencesTheory of Special RelativityHistorical Origin of Special Theory of RelativityMichelson–Morley ExperimentPostulates of Special Theory of RelativityLorentz TransformationsDoppler EffectRelativistic Space–Time (Minkowski Space)Equivalence of Mass and EnergyConservation Laws of Energy and MomentumGeneralization of Newton’s Equation of MotionRelativistic Lagrangian and Hamiltonian FunctionsRelativistic Kinematics of CollisionsCollision Threshold EnergiesReferencesNewtonian Gravity and Newtonian CosmologyNewton’s Law of GravityGravitational Field and Gravitational PotentialGravitational Field Equations: Poisson’s and Laplace’s EquationsGravitational Field and Potential of Extended BodyTidesGeneral Theory of Relativity: Relativistic Theory of GravitationIntroduction to CosmologyBrief History of Cosmological IdeasDiscovery of Expansion of the Universe, Hubble’s LawBig BangFormulating Dynamical Models of the UniverseCosmological Red Shift and Hubble Constant HCritical Mass Density and Future of the UniverseMicrowave Background RadiationDark MatterReferenceHamilton–Jacobi Theory of DynamicsCanonical Transformation and H-J EquationAction and Angle VariablesInfinitesimal Canonical Transformations and Time Development OperatorH-J Theory and Wave MechanicsReferenceIntroduction to Lagrangian and Hamiltonian Formulations for Continuous Systems and Classical FieldsVibration of Loaded StringVibrating Strings and the Wave EquationContinuous Systems and Classical FieldsScalar and Vector of FieldsAppendix 1: Vector Analysis and Ordinary Differential EquationsAppendix 2: D’Alembert’s Principle and Lagrange’s EquationsAppendix 3: Derivation of Hamilton’s Principle from D’Alembert’s PrincipleAppendix 4: Noether’s TheoremAppendix 5: Conic Sections, Ellipse, Parabola, and HyperbolaIndex

AUTORE

Dr. Tai Chow was born and raised in China. He received the Bachelor of Science degree in physics from National Taiwan University, a master’s degree in physics from Case Western Reserve University in Cleveland, and a Ph.D. degree in physics from the University of Rochester in New York. Since 1970, Dr. Chow has been in the Department of Physics at California State University, Stanislaus, and served as the department chairman for 18 years. He has published more than 40 articles in physics and astrophysics journals and is the author of four textbooks.

ALTRE INFORMAZIONI

• Condizione: Nuovo
• ISBN: 9781466569980
• Dimensioni: 10 x 7 in Ø 2.85 lb
• Formato: Copertina rigida
• Illustration Notes: 318 b/w images, 3 tables and approx 1,504 equations
• Pagine Arabe: 639