Intermediate Dynamics

Description

This advanced undergraduate physics textbook presents an accessible treatment of classical mechanics using plain language and clear examples. While comprehensive, the book can be tailored to a one-semester course. An early introduction of the Lagrangian and Hamiltonian formalisms gives students an opportunity to utilize these important techniques in the easily visualized context of classical mechanics. The inclusion of 321 simple in-chapter exercises, 82 worked examples, 550 more challenging end-of-chapter problems, and 65 computational projects reinforce students' understanding of key physical concepts and give instructors freedom to choose from a wide variety of assessment and support materials. This new edition has been reorganized. Numerous sections were rewritten. New problems, a chapter on fluid dynamics, and brief optional studies of advanced topics such as general relativity and orbital mechanics have been incorporated. Online resources include a solutions manual for instructors, lecture slides, and a set of student-oriented video lectures. INTERMEDIATE DYNAMICS Intermediate Dynamics Intermediate Dynamics Second Edition PATRICK HAMILL Organization A One-Semester Course Exercises and Problems Acknowledgments A Brief Review of Introductory Concepts 1.1 Kinematics У Jv = y* aJr. 1.1.1 Motion in a Straight Line at Constant Acceleration Exercise 1.1 1 .2 Newton’s Second Law a = F/m. F = ma. (1.5) 1.3 Work and Energy 1.4 Momentum 1.5 Rotational Motion 1.5.1 Rotational Kinematics 1.5.2 Rotational Dynamics 1.6 Statics 1.7 Rotational Kinetic Energy 1.8 Angular Momentum I = |1| = |r x p| = |rxmv| = rmv sin0, L = £1, = J2(ri x p,). 1.9 Rotational Equivalents N = /a, 1.10 Summary N = r x F. 1 = r x p. 1.11 Problems Computational Projects Kinematics 2.1 Galileo Galilei (Historical Note) 2.2 The Principle of Inertia A body will remain in uniform motion as long as no net external force acts on it. 2.3 Basic Concepts in Kinematics 2.3.1 Motion in One Dimension with Constant Acceleration Exercise 2.1 2.3.2 Projectile Motion 2.3.3 Rotation About a Fixed Axis = -^[(e-c,)(cf+1)-e0(1)] 2.3.4 The Relation between Linear and Rotational Motion vT = (») x r. (2.7) 2.4 The Position of a Particle on a Plane 2.5 Unit Vectors c = a x b a • b = | a | | b | cos(a,b). (2.9) к x i = j, i x к = —j. i J к 2.6 Kinematics in Two Dimensions 2.6.1 Cartesian Coordinates 2.6.2 Plane Polar Coordinates r = r(0), and 2.7 Kinematics in Three Dimensions 2.7.1 Cartesian Coordinates 2.7.2 Cylindrical Coordinates Ф = Ф(0). p • p = 1, ф • ф = 1, к • к = 1, V - Г - £(pp + zk) = pp + + zk. 2.7.3 Spherical Coordinates Ф = Ф(0). Эф . Эф . v = — = — (rr) = —- r + r —, dt dt dt dt 2.8 Summary v = xi + yj + zk, a = xi + yj + zk. r = rr, r = pp + zk, r = rr, 2.9 Problems Army _ 10 Newton’s Laws: Determining the Motion 3.1 Isaac Newton (Historical Note) 3.2 The Law of Inertia A body in motion will remain in uniform motion and a body at rest will remain at rest unless acted upon by a net external force. 3.3 Newtons Second Law and the Equation of Motion The rate of change of the momentum of an isolated body is equal to the net external force applied to it. ^=F, 3.4 Newton s Third Law: Action Equals Reaction To every action there is always opposed an equal reaction. //fc)y = 7.9 Problems Conservation Laws and Symmetries 8.1 Emmy Noether (Historical Note) 8.2 Symmetry 8.3 Symmetry and the Laws of Physics For every symmetry there is a corresponding constant of the motion. 8.4 Symmetries and Conserved Physical Quantities 8.4.1 Conservation of Linear Momentum 8.4.2 Conservation of Energy 8.5 Are the Laws of Physics Symmetrical? 8.5.1 Nonconservation of Parity 8.6 Strangeness (Optional) 8.7 Symmetry Breaking 8.8 Problems Gravity The Gravitational Field 9.1 Newton’s Law of Universal Gravitation - G yr, |r2-ri|2 (9.1) r2 - ri r = . |г2 -ril 17 П - Г2 9.1.1 Universality of the Law of Gravitation 9.1.2 Action at a Distance 9.2 The Gravitational Field 9.3 The Gravitational Field of an Extended Body |x - x'|3 (x-x7)2 M . rj 1 T (4L — x')2 _4L — x'_0 9.4 The Gravitational Potential V(r) Jsurface IГ — r'| J0=O Л=0 IГ — r'| 9.5 Field Lines and Equipotential Surfaces 9.6 The Newtonian Gravitational Field Equations 9.6.1 Gauss’s Law V • g = — 4тгСр. 9.7 The Equations of Poisson and Laplace Vg = - V -V Ф= -V20. V20 = 4тгСр. 9.8 Einstein’s Theory of Gravitation (Optional) 9.9 Summary / F \ r — rz \m / |r — r'p g(r) = -G [ p(r/)———Y—^dTf. Jbody |r —r'| /body |Г- r'| V x g = 0, V2 = 0. 9.10 Problems Computational Technique: Numerical Integration Central Force Motion: The Kepler Problem 10.1 Johannes Kepler (Historical Note) 10.2 Kepler’s Laws 10.3 Central Forces F= 6162 r. The angular momentum is constant. 10.4 The Equation of Motion F = — r 10.5 Energy and the Effective Potential Energy 10.6 Solving the Radial Equation of Motion Sophisticated Technique 10.8 The Equation of an Ellipse 10.9 Kepler’s Laws Revisited The orbit of a planet is an ellipse with the Sun at one of the focal points. The radius vector of a planet sweeps out equal areas in equal times. 10.10 Orbital Mechanics 10.10.1 Energy and Angular Momentum of a Satellite h = \/m = r x v. 10.10.2 The Hohmann Transfer Orbit 10.11 A Perturbed Circular Orbit /(). dt 17.5 Torque-Free Motion 17.6 The Spinning Top (Gyroscope) a> = + 0z + i^z', 7 2 7 2 /isin#o /isim^o Exercise 17.15 17.6.1 Precession without Nutation 2 17.6.2 Nutation 17.7 Summary T = У p(r)(r2l — rr)dr. 17.8 Problems 18 Statics 18.1 Basic Concepts Nc = r x Fc = r x (F« + Ffe) = Nfl + N&, 18.2 Couples, Resultants, and Equilibrants Nq = 12 (rQ' x F' ) ’ nQ' = 12 (rQ'2а’ m+M V-swcos2“7 / g(a-R) “ V (а-Я)На2 2m LЭх2 Эу2 -^-v2 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Chapter 21