Expanding gravitational systems

Saari, Donald G.

doi:10.1090/S0002-9947-1971-0275729-5

Expanding gravitational systems
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by Donald G. Saari

Trans. Amer. Math. Soc. 156 (1971), 219-240

DOI: https://doi.org/10.1090/S0002-9947-1971-0275729-5

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Abstract:

In this paper we obtain a classification of motion for Newtonian gravitational systems as time approaches infinity. The basic assumption is that the motion survives long enough to be studied, i.e., the solution exists in the interval $(0,\infty )$. From this classification it is possible to obtain a sketch of the evolving Newtonian universe.

References

39

R. P. Boas Jr., A Tauberian Theorem Connected with the Problem of Three Bodies, Amer. J. Math. 61 (1939), no. 1, 161–164. MR 1507368, DOI 10.2307/2371395
J. Karamata, Über einen Tauberschen Satz im Dreikörperproblem, Amer. J. Math. 61 (1939), 769–770 (German). MR 63, DOI 10.2307/2371334

Comments on the Sundman inequality

Approximate decoupling in the n-body problem

Harry Pollard, Mathematical introduction to celestial mechanics, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1966. MR 0197175
Harry Pollard, The behavior of gravitational systems, J. Math. Mech. 17 (1967/1968), 601–611. MR 0261826, DOI 10.1512/iumj.1968.17.17036
Harry Pollard, Some nonlinear Tauberian theorems, Proc. Amer. Math. Soc. 18 (1967), 399–401. MR 219946, DOI 10.1090/S0002-9939-1967-0219946-3
Harry Pollard and Donald G. Saari, Singularities of the $n$-body problem. I, Arch. Rational Mech. Anal. 30 (1968), 263–269. MR 231565, DOI 10.1007/BF00281534
Harry Pollard and Donald G. Saari, Singularities of the $n$-body problem. II, Inequalities, II (Proc. Second Sympos., U.S. Air Force Acad., Colo., 1967) Academic Press, New York, 1970, pp. 255–259. MR 0277853
Harry Pollard and Donald G. Saari, Escape from a gravitational system of positive energy, Celestial Mech. 1 (1969/70), 347–350. MR 261827, DOI 10.1007/BF01231139
Harry Pollard and D. G. Saari, An elementary Tauberian theorem of nonlinear type, Proc. Amer. Math. Soc. 24 (1970), 593–594. MR 251168, DOI 10.1090/S0002-9939-1970-0251168-2
Donald G. Saari, On oscillatory motion in the problem of three bodies, Celestial Mech. 1 (1969/70), 343–346. MR 263286, DOI 10.1007/BF01231138

On bounded solutions of the n-body problem

Donald G. Saari, Some large $O$ nonlinear Tauberian theorems, Proc. Amer. Math. Soc. 21 (1969), 459–462. MR 243234, DOI 10.1090/S0002-9939-1969-0243234-4
Carl Ludwig Siegel, Der Dreierstoss, Ann. of Math. (2) 42 (1941), 127–168 (German). MR 3736, DOI 10.2307/1968991
K. Sitnikov, The existence of oscillatory motions in the three-body problems, Soviet Physics Dokl. 5 (1960), 647–650. MR 0127389
Hans J. Sperling, On the real singularities of the $N$-body problem, J. Reine Angew. Math. 245 (1970), 15–40. MR 290630, DOI 10.1515/crll.1970.245.15

Le problème des trois corps

35

The Laplace transform

3

Aurel Wintner, The Analytical Foundations of Celestial Mechanics, Princeton Mathematical Series, vol. 5, Princeton University Press, Princeton, N. J., 1941. MR 0005824