The stability of the triangular Lagrangian points in the general problem of three bodies

The perturbing effects of the Poynting-Robertson drag on motion of an infinitesimal mass around triangular Lagrangian points of the circular restricted three-body problem under small perturbations in the Coriolis and centrifugal forces when the three bodies are oblate spheroids and the primaries are emitters of radiation pressure, is the focus of this paper. The equations governing the dynamical system have been derived and locations of triangular Lagrangian points are determined. It is seen that the locations are influenced by the perturbing forces of centrifugal perturbation and the oblateness, radiation pressure and, P-R drag of the primaries. Using the software Mathematica, numerical analysis are carried out to demonstrate how the dynamical elements: mass ratio, oblateness, radiation pressure, P-R drag and centrifugal perturbation influence the positions of triangular equilibrium points, zero velocity surfaces and the stability. Our investigation reveals that, though the radiation pressure, oblateness and centrifugal perturbation decrease region of stability when motion is stable, however, they are not the influential forces of instability but the P-R drag. In the region when motion around the triangular points are stable an inclusion of the P-R drag of the bigger primary even by an almost negligible value of 1.04548*10-9 overrides other effect and changes stability to instability. Hence, we conclude that the P-R drag is a strong perturbing force which changes stability to instability and motion around triangular Lagrangian points remain unstable in the presence of the P-R drag.

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Parallel Columns With Common Lateral Supports

Journal of Applied Mechanics ◽

10.1115/1.4009495 ◽

1945 ◽

Vol 12 (4) ◽

pp. A253-A256

Author(s):

H. L. Langhaar

Keyword(s):

General Problem ◽

Correlation Effects ◽

Aircraft Structures ◽

Single Column ◽

The Stability ◽

Stress Analyses

Abstract Problems in the stress analyses of semimonocoque aircraft structures have suggested the investigation of the stability of a system of closely spaced, equally stressed, parallel columns with lateral bulkhead supports. The theory presented in this paper establishes a correlation between this problem and the problem of stability of a single column with lateral spring supports. Since the theory for the latter case has been developed by several authors, the correlation effects a solution of the more general problem.

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