Modern Analytic MechanicsSpringer Science & Business Media, 1999. szept. 30. - 341 oldal By modern analytic mechanics we mean the classical mechanics of today, that is, the mechanics that has proven particularly useful in understanding the universe as we experience it from the solar system, to particle accelerators, to rocket motion. The mathematical and numerical techniques that are part of this mechanics that we present are those that we have found to be particularly productive in our work in the subject. The balance of topics in this book is somewhat different from previous texts. We emphasize the use of phase space to describe the dynamics of a system and to have a qualitative understanding of nonlinear systems. We incorporate exercises that are to be done using a computer to solve linear and nonlinear problems and to have a graphical representation of the results. While analytic solutions of physics problems are to be prefer. red, it is not always possible to find them for all problems. When that happens, techniques other than analysis must be brought to bear on the problem. In many cases numerical treatments are useful in generating solutions, and with these solutions often come new insights. These insights can sometimes be used for making further analytic progress, and often the process is iterative. Thus the ability to use a computer to solve problems is one of the tools of the modern physicist. Just as analytic problem-solving enhances the student's understanding of physics, so will using the computer enhance his or her appreciation of the subject. |
Tartalomjegyzék
Newtonian Mechanics | 1 |
13 INERTIAL REFERENCE FRAMES | 3 |
14 MANYPARTICLE SYSTEMS | 6 |
15 ENERGY AND ENERGY CONSERVATION | 12 |
16 ANGULAR MOMENTUM | 17 |
17 THE HARMONIC OSCILLATOR | 20 |
18 MOTION IN NONINERTIAL FRAMES | 28 |
Hamiltons Principle | 33 |
83 ENERGY IN TRAVELING WAVES | 181 |
84 STANDING WAVES | 182 |
85 DISPERSION PHASE VELOCITY AND GROUP VELOCITY | 185 |
86 NUMERICAL SOLUTION OF THE WAVE EQUATION | 187 |
87 WAVES IN TWO DIMENSIONS | 191 |
88 STRESS WAVES IN SOLIDS | 203 |
Special Relativity | 209 |
92 THE LORENTZ TRANSFORMATION | 211 |
23 GENERALIZED COORDINATES | 36 |
24 CONSERVATION THEOREMS | 42 |
25 THE PENDULUM REVISITED OR LAGRANGE MULTIPLIERS | 45 |
Gravitational Law and Planetary Motion | 49 |
CONSERVATION THEOREMS | 54 |
33 ELLIPTICAL TRAJECTORIES AND KEPLERS LAWS | 61 |
34 ORBIT PRECESSION | 63 |
35 STABILITY OF A CIRCULAR ORBIT | 64 |
HYPERBOLIC ORBITS AND ELASTIC SCATTERING | 66 |
Hamiltonian Description | 73 |
43 HAMILTON FUNCTION AND CONSERVATION THEOREMS | 76 |
44 NUMERICAL INTEGRATION OF THE HAMILTON EQUATIONS | 80 |
45 PHASESPACE TRAJECTORIES | 83 |
46 LIOUVILLE THEOREM | 88 |
47 CANONICAL TRANSFORMATIONS | 91 |
48 VIRIAL THEOREM | 92 |
Oscillations I | 95 |
52 SYSTEMS WITH MANY DEGREES OF FREEDOM | 105 |
53 NORMAL MODE ANALYSIS | 112 |
54 DIAGONALIZATION OF THE MASS MATRIX | 114 |
55 DRIVEN OSCILLATORS | 119 |
Oscillations II | 121 |
62 FOCUSING OF CHARGED PARTICLES | 132 |
6J NONLINEAR OSCILLATIONS | 138 |
64 THE BOUNCING BALL | 140 |
Rigid Bodies | 147 |
72 EQUATIONS OF MOTION OF A RIGID BODY | 148 |
73 VELOCITY AND ANGULAR VELOCITY | 152 |
74 MOMENTUM AND ANGULAR MOMENTUM OF A RIGID BODY | 155 |
76 KINETIC ENERGY AND THE INERTIA TENSOR | 156 |
77 DIAGONALIZATION OF THE INERTIA TENSOR | 158 |
78 TRANSFORMATION OF THE INERTIA TENSOR | 159 |
79 EULERS EQUATIONS OF MOTION | 161 |
710 FREE MOTION OF A RIGID BODY | 163 |
711 EULERS ANGLES | 165 |
712 MOTION OF A HEAVY SYMMETRICAL TOP WITH ONE POINT FIXEDe1 | 166 |
713 STABILITY OF RIGID BODY ROTATION | 172 |
Waves in Mechanical Systems | 175 |
82 REFLECTED AND TRANSMITTED WAVES | 177 |
93 TRANSFORMATION OF VELOCITY AND ACCELERATION | 215 |
94 SIMULTANEITY TIME DILATION AND LORENTZFITZGERALD CONTRACTION | 217 |
95 FOURVECTOR FORMALISM | 222 |
96 ENERGYMOMENTUM FOURVECTOR | 227 |
97 DOPPLER EFFECT | 228 |
98 PARTICLE DYNAMICS | 230 |
99 THE LORENTZ FORCE | 233 |
910 SOLUTIONS OF THE EQUATIONS OF MOTION | 235 |
Problems | 243 |
102 HAMILTONS PRINCIPLE Chapter 2 | 248 |
103 GRAVITATIONAL LAW AND PLANETARY MOTION Chapter 3 | 251 |
104 HAMILTONIAN DESCRIPTION Chapter 4 | 254 |
105 OSCILLATIONS Chapters 5 and 6 | 256 |
106 RIGID BODIES Chapter 7 | 260 |
107 WAVES IN MECHANICAL SYSTEMS Chapter 8 | 262 |
108 SPECIAL RELATIVITY Chapter 9 | 266 |
Linear Algebra | 269 |
A1 PROPERTIES OF DETERMINANTS | 270 |
A3 MATRIX OPERATIONS | 273 |
A4 TYPES OF MATRICES | 274 |
Linear Differential Equations | 277 |
Numerical Methods | 283 |
C2 NUMERICAL INTEGRATION OF ORDINARY DIFFERENTIAL EQUATIONS | 286 |
Fourier Series | 299 |
D2 EVALUATION OF SERIES | 301 |
D3 NUMERICAL EVALUATION OF SERIES COEFFICIENTS | 302 |
D4 COMPLEX SERIES | 305 |
Computer Exercises in Classical Mechanics | 307 |
E2 STARTING OUT | 308 |
FORTRAN | 323 |
F2 OTHER DATA TYPES | 326 |
F4 LOOPING | 329 |
F5 VARIABLES WITH MANY VALUES | 330 |
F6 SUBROUTINES | 332 |
Mathcad | 333 |
Bibliography | 337 |
339 | |
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2eam amplitude angle angular momentum angular velocity assume axes axis calculate center of mass coefficients components conservation const constant coordinates defined describing determine differential equations direction displacement distance double precision eigenvectors equal equation of motion equilibrium point evaluate example EXERCISE Figure FORTRAN four-vector frequency function Galilean transformation gravitational Hamilton equations Hamiltonian harmonic oscillator inertia tensor inertial frame initial conditions integral kinetic energy Lagrangian last equation leapfrog integration length Let us consider linear Lorentz transformation m₁ m₂ Mathcad matrix obtain orbit particle of mass pendulum plane plot position potential energy problem quantity r₁ radius Real Double reference frame result rewrite rigid body rocket rotation Show shown in Fig solution solve speed string subroutine t₁ theorem transformation V₁ variables vector vertical wave equation write written x-axis x₁ zero дн дх