Author | Grossman, Nathaniel. author |
---|---|
Title | The Sheer Joy of Celestial Mechanics [electronic resource] / by Nathaniel Grossman |
Imprint | Boston, MA : Birkhรคuser Boston, 1996 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-4090-7 |
Descript | XVIII, 182 p. online resource |
I. Rotating Coordinates -- 1. Some kinematics -- 2. Dynamics -- 3. Newtonโs 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. Foucaultโs pendulum -- II. Central Forces -- 1. Motion in a central field -- 2. Force and orbit -- 3. The integrable cases of central forces -- 4. Bonnetโs Theorem -- 5. Miscellaneous exercises -- 6. Motion on a surface of revolution -- III. Orbits under the Inverse Square Law -- 1. Keplerโs three laws and Newtonโs Law -- 2. The orbit from Newtonโs Law -- 3. The true, eccentric, and mean anomalies -- 4. Keplerโs equation -- 5. Solution of Keplerโs 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. Lagrangeโs 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. Bertrandโs 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. Eulerโs equations of motion -- 5. Euler free motion of the Earth -- 6. Feynmanโs 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; MacCullaghโs 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. Poincarรฉโs inequality for rotating fluids -- 6. Liechtensteinโs symmetry theorem -- 7. Rotundity of a rotating fluid -- 8. Ellipsoidal figures of rotating fluids