Astronomy and Astrophysics – Astronomy
Scientific paper
Mar 1977
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977acaau...4..271w&link_type=abstract
Acta Astronautica, Volume 4, Issue 3-4, p. 271-277.
Astronomy and Astrophysics
Astronomy
Scientific paper
The total stability of lunar librational motion is studied in this paper. The analysis is made by extending the concept of Liapunov stability to that of total stability, or stability under constantly acting disturbances, as first introduced by Doubochine. The equations of librational motion in the absence of disturbing torques are expressed in the first-order vector form x′(τ) =f(x, τ), where x(τ) represents the motion from the Earth-pointing equilibrium. By adding an expression for external disturbing torques this equation becomes x′(τ) =f(x, τ) +g(x, τ). Expressions are found for δ1(ɛ) and δ2(ɛ) such that if x(t) is a solution to the perturbed equation, if |x(τ0)| < δ1(ɛ) and if (in a certain neighborhood of the equilibrium) |g(x, τ)| < δ2(ɛ), then |x(τ)| < ɛ for all τ ⩾ τ0. The expressions for the bounds δ1 and δ2 depend on physical parameters of the Moon.
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