Ja n 20 04 Average Angular Velocity Hanno Essén

The Physics of Rotational Flattening and the Point Core Model

A point mass at the center of an ellipsoidal homogeneous fluid is used as a simple model to study the effect of rotation on the shape and external gravitational field of planets and stars. Maclaurin’s analytical result for a homogenous body is generalized to this model. The absence of a third order term in the Taylor expansion of the Maclaurin function leads to further simple but very accurate ...

ar X iv : m at h - ph / 0 50 10 33 v 1 1 2 Ja n 20 05 Indefinite metric

Magnetic Field and Current Are Zero inside Ideal Conductors

We prove a theorem on the magnetic energy minimum in a system of perfect, or ideal, conductors. It is analogous to Thomson’s theorem on the equilibrium electric field and charge distribution in a system of conductors. We first prove Thomson’s theorem using a variational principle. Our new theorem is then derived by similar methods. We find that magnetic energy is minimized when the current dist...

ar X iv : m at h / 04 01 12 6 v 1 [ m at h . N T ] 1 3 Ja n 20 04 THREE LECTURES ON THE RIEMANN ZETA - FUNCTION

qc / 0 50 10 44 v 1 1 2 Ja n 20 05 Rotating Fluids with Self - Gravitation in Bounded Domains ∗

In this paper, we study the steady solutions of Euler-Poisson equations in bounded domains with prescribed angular velocity. This models a rotating Newtonian star consisting of a compressible perfect fluid with given equation of state P = eSργ . When the domain is a ball and the angular velocity is constant, we obtain both existence and non-existence theorems, depending on the adiabatic gas con...