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On the part of the motion of the lunar perigee which is a function of the mean motions of the Sun and the Moon. (On the part of the motion of the lunar perigee which is a function of the mean motions of the Sun and the Moon.) (English) JFM 18.1106.01

Die Arbeit ist im wesentlichen ein Abdruck einer früheren aus dem Jahre 1877 (vgl. F. d. M. IX. 795, JFM 09.0795.01). Es mag deshalb hier nur bemerkt werden, dass das an sich sinnreiche, aber wenig strenge Verfahren des Herrn Verfassers zur Integration der Differentialgleichung \[ \frac {d^2x}{dt^2} + x.X = 0, \]
\[ X = a_0 + a_1\cos t + a_2\cos 2t + \cdots, \] seitdem durch strenge Entwickelungen ersetzt worden ist (vgl. F. d. M. 1883. XV. 980-981, JFM 15.0980.03).

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[1] AsJacobi was the first to announce this integral (Comptes rendus de l’aeadémie des sciences de Paris, Tome III, p. 59), we shall take the liberty of calling it the Jacobian integral.
[2] These expressions are established in another memoir. See American Journal of Mathematics, Vol. I, p. 138.
[3] A similar condition of things occurs in many less complex problems for instance, in the determination of the principal axes of rotation of a rigid body. Although there is but one set of such axes, yet the final equation, solving the question, is of the third degree, all because analysis knows no distinction between the axes ofx, y andz.
[4] On the general integrals of planetary motion, Smithsonian Contributions to Knowledge, No. 281, p. 31.
[5] See American Journal of Mathematics, Vol. I, p. 247.
[6] See American Journal of Mathematics, Vol. I, p. 249.
[7] Comptes rendus de l’académie des sciences de Paris, Tome LXXIV, p. 19.
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