Computer Science
Scientific paper
Dec 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994icar..112..465m&link_type=abstract
Icarus (ISSN 0019-1035), vol. 112, no. 2, p. 465-484
Computer Science
37
Circles (Geometry), Drag, Lagrangian Equilibrium Points, Motion Stability, Position (Location), Three Body Problem, Jacobi Integral, Poynting-Robertson Effect, Series Expansion, Taylor Series
Scientific paper
The location and stability of the five Lagrangian equilibrium points in the planar, circular restricted three-body problem are investigated when the third body is acted on by a variety of drag forces. The approximate locations of the displaced equilibrium points are calculated for small mass ratios and a simple criterion for their linear stability is derived. If a1 and a3 denote the coefficients of the linear and cubic terms in the characteristic equation derived from a linear stability analysis, then an equilibrium point is asymptotically stable provided 0 less than a1 is less than a3. In cases where a1 is approximately equal to 0 or a1 is approximatley equal to a3 the point is unstable but there is a difference in the e- folding time scales of the shifted L4 and L5 points such that the L4 point, if it exists, is less unstable than the L5 point. The results are applied to a number of general and specific drag forces. It is shown that, contrary to intuition, certain drag forces produce asymptotic stability of the displaced triangular equilibrium points, L4 and L5. Therefore, simple energy arguments alone cannot be used to determine stability in the restricted problem. The shifted equilibrium points of all drag forces have x and y components in the rotating frame of the form (-kg*y, +kg*x) evaluated when dot x = dot y = 0, where g* is a function of x and y, follow identical, near-circular paths for increasing drag.
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