An Introduction to the Theory of Newtonian Attraction
This book is intended for students taking an honours course in mathematics (Master's degree), but the arrangement of the material is suitable for the pass degree candidate. Several of the theorems in pure mathematics specially required for the subject are brought together in Chapter 1; the more difficult chapters on Green's theorem, harmonic functions and the attraction of ellipsoids come at the end. Examples are grouped according to difficulty. --Back cover.
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ATTRACTION AND POTENTIAL
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astronomical unit attracting matter attracting particles axes axis body boundary centre of gravity closed surface co-ordinates coefficients components of attraction const cylinder denotes the mass differentiating distribution of matter ellipsoid ellipticity enclosed equal equilibrium equipotential surfaces exert expression external point Find the potential finite Gauss's theorem given grad gravitational constant Green's function Green's theorem harmonic function Hence homogeneous infinite sphere internal Laplace's equation layer London Univ mass per unit oblate spheroid outward flux parallel perpendicular points inside Poisson's equation potential energy potential function Prove region bounded resultant attraction right angles semi-axes Shew solid angle solid harmonic solution of Laplace's space sphere of radius surface density surface harmonics surface integrals tangent plane thin spherical shell tion uniform circular uniform density uniform solid sphere uniform sphere unit area unit length unit mass vanishes vector vertex volume density volume integrals zero