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The critical inclination in artificial satellite theory

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A delicacy so very susceptible of offence...—Hester Lynch PIOZZI,Observations and Reflections made in the Course of a Journey through France, Italy and Germany (1789)

Abstract

Certain it is that the critical inclination in the main problem of artificial satellite theory is an intrinsic singularity. Its significance stems from two geometric events in the reduced phase space on the manifolds of constant polar angular momentum and constant Delaunay action. In the neighborhood of the critical inclination, along the family of circular orbits, there appear two Hopf bifurcations, to each of which there converge two families of orbits with stationary perigees. On the stretch between the bifurcations, the circular orbits in the planes at critical inclinmation are unstable. A global analysis of the double forking is made possible by the realization that the reduced phase space consists of bundles of two-dimensional spheres. Extensive numerical integrations illustrate the transitions in the phase flow on the spheres as the system passes through the bifurcations.

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Author notes

  1. Shannon L. Coffey

    Present address: U.S. Naval Research Laboratory, 20375, Washington, D.C.

Authors and Affiliations

  1. National Bureau of Standards, 20899, Gaithersburg, MD, U.S.A.

    Shannon L. Coffey, André Deprit & Bruce R. Miller

Authors
  1. Shannon L. Coffey
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  2. André Deprit
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  3. Bruce R. Miller
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NAS/NRC Postgraduate Research Associate in 1984–1985.

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Coffey, S.L., Deprit, A. & Miller, B.R. The critical inclination in artificial satellite theory. Celestial Mechanics 39, 365–406 (1986). https://doi.org/10.1007/BF01230483

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