Dear Reader, Here is your book. Take it, run with it, pass it, punt it, enjoy all the many things that you can do with it, but-above all-read it. Like all textbooks, it was written to help you increase your knowledge; unlike all too many textbooks that you have bought, it will be fun to read. A preface usually tells of the author's reasons for writing the book and the author's goals for the reader, followed by a swarm of other important matters that must be attended to yet fit nowhere else in the book. I am fortunate in being able to include an insightful prepublication review that goes directly to my motivations and goals. (Look for it following this preface.) That leaves only those other important matters. In preparing the text, I consulted a number of books, chief of which included these: - S. Chandrasekhar, Ellipsoidal Figures of Equilibrium, Yale Uni versity Press, 1969. - J .M.A. Danby, Fundamentals of Celestial Mechanics, Macmil lan, 1962. Now available in a 2nd edition, 3rd printing, revised, corrected and enlarged, Willmann-Bell, 1992. - Y. Hagihara, Theories of Equilibrium Figures of a Rotating Ho mogeneous Fluid Mass, NASA, 1970. - R.A. Lyttleton, The Stability of Rotating Liquid Masses, C- ix x PREFACE bridge University Press, 1953. - C.B. Officer, Introduction to Theoretical Geophysics, Springer Verlag, 1974. - A.S. Ramsey, Newtonian Attraction, Cambridge University Press, 1949. - W.M. Smart, Celestial Mechanics, Longmans, Green, and Co, 1953.
I. Rotating Coordinates.- 1. Some kinematics.- 2. Dynamics.- 3. Newton's Laws of Motion.- 4. The Laws of Motion and conservation laws.- 5. Simple harmonic motion.- 6. Linear motion in an inverse square field.- 7. Pendulum in a uniform gravitational field.- 8. Foucault's pendulum.- II. Central Forces.- 1. Motion in a central field.- 2. Force and orbit.- 3. The integrable cases of central forces.- 4. Bonnet's Theorem.- 5. Miscellaneous exercises.- 6. Motion on a surface of revolution.- III. Orbits under the Inverse Square Law.- 1. Kepler's three laws and Newton's Law.- 2. The orbit from Newton's Law.- 3. The true, eccentric, and mean anomalies.- 4. Kepler's equation.- 5. Solution of Kepler's equation.- 6. The velocity of a planet in its orbit.- 7. Drifting of the gravitational constant.- IV. Expansions for an Elliptic Orbit.- 1. The general problem.- 2. Lagrange's expansion theorem.- 3. Bessel coefficients.- 4. Fourier series.- 5. Preliminaries for expansions.- 6. Some algebraically-derived expansions.- 7. Expansions in terms of the mean anomaly.- V. Gravitation and Closed Orbits.- 1. Bertrand's characterization of a universal gravitation.- 2. Circular motions.- 3. Neighbors of circular motions.- 4. Higher perturbations; completion of the proof.- 5. From differential geometry in the large.- 6. Ovals described under a central attraction.- VI. Dynamical Properties of Rigid Bodies.- 1. From discrete to continuous distributions of mass.- 2. Moments of inertia.- 3. Particular moments of inertia.- 4. Euler's equations of motion.- 5. Euler free motion of the Earth.- 6. Feynman's wobbling plate.- 7. The gyrocompass.- 8. Euler angles.- VII. Gravitational Properties of Solids.- 1. The gravitational potential of a sphere.- 2. Potential of a distant body; MacCullagh's formula.- 3. Precession of the equinoxes.- 4. Internal potential of a homogeneous ellipsoid.- 5. External potential of a homogeneous ellipsoid.- VIII. Shape of a Self-Gravitating Fluid.- 1. Hydrostatic equilibrium.- 2. Distortion of a liquid sphere by a distant mass.- 3. Tide-raising on a ringed planet.- 4. Clairaut and the variation of gravity.- 5. Poincaré's inequality for rotating fluids.- 6. Liechtenstein's symmetry theorem.- 7. Rotundity of a rotating fluid.- 8. Ellipsoidal figures of rotating fluids.
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