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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.
These expressions are established in another memoir. See American Journal of Mathematics, Vol. I, p. 138.
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.
On the general integrals of planetary motion, Smithsonian Contributions to Knowledge, No. 281, p. 31.
See American Journal of Mathematics, Vol. I, p. 247.
See American Journal of Mathematics, Vol. I, p. 249.
Comptes rendus de l'académie des sciences de Paris, Tome LXXIV, p. 19.
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Reprinted, with som additions from a paper published at Cambridge U.S.A., 1877.
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Hill, G.W. On the part of the motion of the lunar perigee which is a function of the mean motions of the sun and moon. Acta Math. 8, 1–36 (1886). https://doi.org/10.1007/BF02417081
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DOI: https://doi.org/10.1007/BF02417081