Abstract
A new formula for the angular velocity of equilibrium figures of a self-gravitating rotating fluid mass is derived. An important feature of this formula is that the angular velocity is expressed in terms of the components of the inner and outer gravitational energy of the figure introduced by us earlier. We proved the adequacy of the new formula by establishing that it gives correct values of angular velocity in important special cases for sequences of homogeneous classical Maclaurin spheroids and Jacobi triaxial ellipsoids. The advantage of the new formula is that it can describe not only uniform ellipsoid equilibrium figures, but also equilibrium figures of any other geometric form, including toroidal and non-ellipsoidal configurations. This formula extends the application of the theory of equilibrium figures and provides additional possibilities for studying the equilibrium and stability of complex dynamical systems.
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Kondratyev, B.P. The new formula for the angular velocity of rotating equilibrium figures. Astrophys Space Sci 368, 84 (2023). https://doi.org/10.1007/s10509-023-04239-6
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DOI: https://doi.org/10.1007/s10509-023-04239-6