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. Language: English