Convergence of Liapunov Series for Maclaurin Ellipsoids

Details Convergence of Liapunov Series for Maclaurin Ellipsoids Convergence of Liapunov Series for Maclaurin Ellipsoids

Sep 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002cemda..84...57k&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, v. 84, Issue 1, p. 57-63 (2002).

Astronomy and Astrophysics

Astronomy

3

Figures Of Equilibrium, Maclaurin Ellipsoids, Liapunov Series, Convergence Radius

Scientific paper

According to the classical theory of equilibrium figures surfaces of equal density, potential and pressure concur (let call them isobars). Isobars may be represented by means of Liapunov power series in small parameter q, up to the first approximation coincident with centrifugal to gravitational force ratio on the equator. A. M. Liapunov has proved the existence of the universal convergence radius q*: above mentioned series converge for all bodies if |q| < q*. Using Liapunov's algorithm and symbolic calculus tools we have calculated q* = 0.000370916. Evidently, convergence radius q0 may be much greater in non-pathological situations. We plan to examine several simplest cases. In the present paper, we find q0 for homogeneous liquid. The convergence radius turns out to be unexpectedly large coinciding with the upper boundary value q0 = 0.337 for Maclaurin ellipsoids.

Affiliated with

Also associated with

No associations

Rating

Convergence of Liapunov Series for Maclaurin Ellipsoids does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Convergence of Liapunov Series for Maclaurin Ellipsoids, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Convergence of Liapunov Series for Maclaurin Ellipsoids will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-1312858