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On the manifolds of total collapse orbits and of completely parabolic orbits for the n-body problem. (English) Zbl 0475.70010


MSC:

70F10 \(n\)-body problems
70F35 Collision of rigid or pseudo-rigid bodies
70M20 Orbital mechanics
70G10 Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics

Citations:

Zbl 0353.70007
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Full Text: DOI

References:

[1] Chazy, I. J., Sur l’allure du mouvement dans le problème des trois corps quand le temps croit indéfiniment, Ann. Sci. École Norm. Sup., 39, 29-130 (1922) · JFM 48.1074.04
[2] Hulkower, N. D., The zero energy three body problem, Indiana Univ. Math. J., 27, 409-448 (1978) · Zbl 0353.70007
[3] Johnson, C. R., The inertia of a product of two hermitian matrices, J. Math. Anal. Appl., 57, 85-90 (1977) · Zbl 0356.15011
[4] Marchal, C.; Saari, D. G., On the final evolution of the \(n\) body problem, J. Differential Equations, 20, 150-186 (1976) · Zbl 0336.70010
[5] Palmore, J., Measure of degenerate relative equilibria, I, Ann. of Math., 104, 421-431 (1976) · Zbl 0321.58014
[6] Pollard, H., Gravitational systems, J. Math. Mech., 17, 601-612 (1976) · Zbl 0159.26102
[7] Pollard, H.; Saari, D. G., Singularities of the \(n\)-body problem, I, Arch. Rational Mech. Anal., 30, 263-269 (1968) · Zbl 0174.26904
[8] Pollard, H.; Saari, D. G., Singularities of the \(n\)-body problem, II, (Shishu, O., Inequalities, Vol. II (1970), Academic Press: Academic Press New York) · Zbl 0174.26904
[9] Saari, D. G., Expanding gravitational systems, Trans. Amer. Math. Soc., 156, 219-240 (1971) · Zbl 0215.57001
[10] Saari, D. G., On the role and the properties of \(n\) body central configurations, Celestial Mech., 21, 9-20 (1980) · Zbl 0422.70014
[12] Siegel, C. L.; Moser, J. K., Lectures on Celestial Mechanics (1971), Springer-Verlag: Springer-Verlag New York · Zbl 0312.70017
[13] Winter, A., The Analytical Foundations of Celestial Mechanics (1941), Princeton Univ. Press: Princeton Univ. Press Princeton, N J · JFM 67.0785.01
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