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This equation was first given by Hamilton, Phil. Trans. Roy. Soc. (1834), II, p. 247, a year before the paper containing what are now called Hamilton's equations. Hamilton's discussion, however, was somewhat more involved than that given here, and it was clarified andgeneralized by Jacobi in his lectures in the winter of 1842–43 (see Jacobi 1869). For somewhat condensed discussions of the theory's development see Dugas 1955 and Lanczos 1970.
G.M.Clemence, Revs. Mod. Phys. 19, 361 (1947).
The generally accepted value was that of S. Newcomb, Wash. Astron. Papers 6, 108 (1898), who gave 41.24″ ±2.09″. The effect had first been established as 36″ by U.J.J. Leverrier in 1859.
I.I. Shapiro in Hegyi 1973.
I.I. Shapiro, G.H. Pettengill, M.E. Ash, R.P. Ingalls, D.B. Campbell, and R.B. Dyce, Phys. Rev. Lett. 28, 1594 (1972).
We restrict ourselves to situations in which ∂/∂ = 0, since they are of principal interest to physicists. For an excellent discussion of the general case as well as the one presented here, see Goldstein 1950, Ch. 9.
P.M. Campbell, Am. J. of Phys. 37, 1161 (1969).
M.Hénon and C.Heiles, Astron. J. 69, 73 (1964); see also M.Hénon, Quart. J. Appl. Math. 27, 291 (1969); E.M.McMillan in Brittin and Odabasi 1971; and J.Ford, Advances in Chem. Phys. 24, 187 (1973).
F.G.Gustavson, Astron. J. 71, 670 (1966).
L.P.Eisenhart, Phys. Rev. 45, 427 (1934). See also Phys. Rev. 74, 87 (1948).
An introduction to Hamilton-Jacobi perturbation theory is given by T.L.Ferrell, Am. J. Phys. 39, 622 (1971).
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(1979). The Hamilton-Jacobi theory. In: Classical Dynamics and Its Quantum Analogues. Lecture Notes in Physics, vol 110. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0021210
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