Secular Stability of Rapidly Rotating Stars of Arbitrary Structure.
Contributor(s)NAVAL RESEARCH LAB WASHINGTON D C OPERATIONS RESEARCH BRANCH
Equations of motion
Partial differential equations
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AbstractThe report uses Poincare's criteria to investigate the secular stability of self-gravitating configurations of arbitrary structure in the state of rapid rotation. The potential energy, a knowledge of which is necessary for application of these criteria, has been determined by an extension of Clairaut's method, and its evaluation in terms of suitably chosen generalized coordinates carried out explicitly to quantities of fourth order in superficial oblateness, for configurations of arbitrary internal structure. The method employed can, moreover, clearly be extended to attain accuracy of any order, at the expense of mere manipulative work which lends itself to machine automation. The angular velocity of axial rotation can be an arbitrary function of position as well as of the time. An application of the results to homogeneous configurations in rigid-body rotation was undertaken to demonstrate that the method, when applied to a case for which a closed solution exists, leads to results which are consistent with it. (Author)