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The Sheer Joy of Celestial Mechanics

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 pref...

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Bibliographic Details
Main Author: Grossman, Nathaniel
Format: eBook
Language:English
Published: Boston, MA Birkhäuser 1996, 1996
Edition:1st ed. 1996
Subjects:
Mathematical Analysis
Astronomy / Observations
Analysis
Astronomy, Cosmology And Space Sciences
Astronomy, Observations And Techniques
Astrophysics
Astronomy
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 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
  • 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. 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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