Bibliography. [1] Howard Anton. Elementary Linear Algebra. John Wiley, New York, QA251.A57 ISBN

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1 Bibliography [1] Howard Anton. Elementary Linear Algebra. John Wiley, New York, QA251.A57 ISBN [2] V. I. Arnol d. Math. Methods of Classical Mechanics. Springer-Verlag, New York, QA805.A6813. [3] R. Creighton Buck. Advanced Calculus. McGraw-Hill, [4] Tohru Eguchi, Peter B. Gilkey, and Andrew J. Hanson. Gravitation, gauge theories and differential geometry. Physics Reports, 66, No. 6: , Doubtless there are more appropriate references, but I learned this here. [5] A. P. French. Special Relativity. W. W. Norton, New York, SBN [6] Herbert Goldstein. Classical Mechanics. Addison-Wesley, Reading, Massachusetts, second edition, QA805.G6. [7] I. S. Gradshtein and I. M. Ryzhik. Table of integrals, series, and products. Academic Press, New York, QA55.R943. [8] Jorge V. Josè and Eugene J. Saletan. Classical Mechanics, a Comtemporary Approach. Cambridge University Press, QC805.J73 ISBN [9] L Landau and Lifschitz. Mechanics. Pergamon Press, Oxford, 2nd edition, QA805.L283/1976. [10] Jerry B. Marion and Stephen T. Thornton. Classical Dynamics. Harcourt Brace Jovanovich, San Diego, 3rd ed edition, QA845.M38/

2 272 BIBLIOGRAPHY [11] R. A. Matzner and L. C Shepley. Classical Mechanics. Prentice Hall, Englewood Cliffs, NJ, 91. QC125.2.M37 ISBN [12] L. Prandtl and O. G. Tietjens. Applied Hydro- and AeroMechanics. Dover Publications, New York, NY, QA911.T564F. [13] Morris Edgar Rose. Elementary Theory of Angular Momentum. Wiley, New York, QC174.1.R7. [14] Walter Rudin. Principles of Mathematical Analysis. McGraw-Hill, New York, [15] James H. Smith. Introduction to Special Relativity. W. A. Benjamin, Inc, New York, [16] M. Spivak. Differential Geometry, volume 1. Publish or Perish, Inc., [17] Keith R. Symon. Mechanics. Addison-Wesley, Reading, Massachusetts, 3rd edition, QC125.S98/1971 ISBN [18] John R. Taylor. Classical Mechanics. University Science Books, Sausalito, California, QC125.2.T ISBN X. [19] O. G. Tietjens. Fundamentals of Hydro- and Aero-Mechanics. Maple Press, York, PA, QA911.T564F. [20] Eugene Wigner. Group Theory and Its Applications to Quantum Mechanics of Atomic Spectra. Academic Press, New York, 1959.

3 Index O(N), 89 1-forms, 156 accoustic modes, 141 action, 45 action-angle, 195 active, 88 adiabatic invariant, 226 angular momentum, 8 antisymmetric, 95 apogee, 72 apsidal angle, 75 associative, 91 attractor, 27 autonomous, 22 bac-cab, 76, 98, 265 Bernoulli s equation, 152 body cone, 108 body coordinates, 86 Born-Oppenheimer, 126 bulk modulus, 147 composition, 89 conditionally periodic motion, 203 configuration space, 5, 44 conformal, 122 conservative force, 7 conserved, 5 conserved quantity, 6 continuum limit, 138 contravariant, 244 cotangent bundle, 20 covariant, 244 current, 253 current conservation, 253 D Alembert s Principle, 40 deviatoric part, 147 diffeomorphism, 186 differential cross section, 81 differential k-form, 170 Dirac delta function, 142 dynamical balancing, 105 dynamical systems, 22 canonical transformation, 162 canonical variables, 162 center of mass, 9 centrifugal barrier, 68 Chandler wobble, 111 closed, 174 closed under, 91 complex structure on phase space, eccentricity, 72 electrostatic potential, 56 elliptic fixed point, 30 elliptic integral, 33 Emmy Noether, 247 enthalpy, 158 equation of continuity, 151 ergodicity, 205

4 274 INDEX Euler s equation, 152 Euler s equations, 107 Euler s Theorem, 92 exact, 156, 174 extended phase space, 6, 180 exterior derivative, 173 exterior product, 170 fixed points, 26 form invariant, 188 free energy, 158 functional, 45 gauge invariance, 57 gauge transformation, 57 generalized force, 17 generalized Hooke s law, 147 generalized momentum, 48 generating function of the canonical transformation, 182 generator, 95 Gibbs free energy, 158 glory scattering, 82 group, 91 group multiplication, 91 Hamilton s characteristic function, 191 Hamilton s equations of motion, 52 Hamilton s principal function, 191 Hamilton-Jacobi, 191 Hamiltonian, 51, 157 Hamiltonian density, 239 hermitean conjugate, 118 herpolhode, 110 Hodge dual, 258 holonomic constraints, 13 Hooke s constant, 148 hyperbolic fixed point, 28 identity, 91 ignorable coordinate, 48 impact parameter, 79 independent frequencies, 204 inertia ellipsoid, 109 inertia tensor, 98 inertial coordinates, 86 integrable system, 201 integral of the motion, 201 intrinsic spin, 189 invariant plane, 109 invariant sets of states, 26 invariant torus, 207 inverse, 87, 91 involution, 201 Jacobi identity, 166 kinetic energy, 7 Knonecker delta, 87 lab angle, 108 Lagrangian, 36 Lagrangian density, 142, 233 Laplace-Runge-Lenz vector, 76 Legendre transformation, 157 Levi-Civita, 95 Lie algebra, 168 line of nodes, 112 Liouville s theorem, 169 logistic equation, 22 magnetic vector potential, 56 major axis, 72 mass matrix, 19, 53 material description, 150 mean motion Hamiltonian, 227 minor axis, 72 moment of inertia, 100

5 INDEX 275 momentum, 5 natural symplectic structure, 179 non-degenerate, 180 nondegenerate system, 204 normal modes, 124 nutation, 117 oblate, 111 optical modes, 141 orbit, 5 orbital angular momentum, 189 order of the dynamical system, 22 orthogonal, 87 parallel axis theorem, 100 passive, 87 perigee, 72 period, 23 periodic, 23 perpendicular axis theorem, 103 phase curve, 21, 26 phase point, 21, 25 phase space, 6, 20 phase trajectory, 182 Poincaré s Lemma, 175 point transformation, 38, 162 Poisson bracket, 165 Poisson s theorem, 169 polhode, 109 potential energy, 7 precessing, 117 precession of the perihelion, 73 principal axes, 104 pseudovector, 96 rainbow scattering, 81 reduced mass, 66 relation among the frequencies, 204 rotation, 89 rotation about an axis, 89 scattering angle, 79 semi-major axis, 72 separatrix, 30 sign of the permutation, 170 similar, 118 similarity transformation, 118 spatial description, 150 stable, 26, 29 Stokes Theorem, 177 strain tensor, 146 stream derivative, 37, 150 stress tensor, 145 stress-energy, 237 strongly stable, 27 structurally stable, 26 subgroup, 92 summation convention, 166 surface force, 145 symplectic, 163 symplectic structure, 22, 159 terminating motion, 27 torque, 8 total external force, 10 total mass, 9 total momentum, 9 trajectory, 5 transpose, 87, 118 turning point, 69, 70 unimodular, 91 unperturbed system, 210 unstable, 28 velocity function, 21 vibrations, 127

6 276 INDEX virtual displacement, 39 viscosity, 151 volume forces, 144 wave numbers, 140 wedge product, 170 work, 7 Young s modulus, 148