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Ellipsoidal Harmonics by George Dassios

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13Applications to physics

In the present chapter we solve some boundary value problems of physical interest in the asymmetric environment that is described by the ellipsoidal geometry. More precisely, we solve: (i) the problem of thermal equilibrium of an ellipsoidal body, which was the problem that gave rise to the theory of ellipsoidal harmonics [223] as well as to the introduction of the general curvilinear system [228]; (ii) the problem of gravitational attraction by a homogeneous ellipsoid, which was an important problem of Newtonian Mechanics for many years and was finally solved by Jacobi, Gauss, Rodrigues, and others in the early nineteenth century [51]; (iii) the problem of an ellipsoidal perfect conductor [329]; (iv) the problem of ...

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