The global solution of the N-body problem
- Wang Qiu-Dong
- … show all 1 hide
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
The problem of finding a global solution for systems in celestial mechanics was proposed by Weierstrass during the last century. More precisely, the goal is to find a solution of the n-body problem in series expansion which is valid for all time. Sundman solved this problem for the case of n = 3 with non-zero angular momentum a long time ago. Unfortunately, it is impossible to directly generalize this beautiful theory to the case of n > 3 or to n = 3 with zero-angular momentum.
A new ‘blowing up’ transformation, which is a modification of McGehee's transformation, is introduced in this paper. By means of this transformation, a complete answer is given for the global solution problem in the case of n > 3 and n = 3 with zero angular momentum.
- Siegel, C.L. and Moser, J.K.: 1971, Lecture on Celestial Mechanics, Springer-Verlag.
- Sundman, K.F.: 1913, ‘Mémoire sur le problème des trois corps’, Acta Math. 36, 105–179.
- McGehee, R.: 1974, ‘Triple collision in the collinear three-body problem’, Invent. Math. 27, 191–277.
- Mather, J.N. and McGehee, R.: 1974, ‘Solution for collinear four-body problem which becomes unbounded in finite time’, Dynamical Systems, Theory and Applications (Rencontres, Battelle Res. Inst. Seattle, Wash.) pp. 573–597.
- Pollard, H.: 1967, ‘Gravitational system’, J. Math. 17, 601–612.
- Saari, D.G.: 1971, ‘Expanding gravitational system’, Trans. Amer. Math. Soc. 156, 219–240.
- Marchel, C. and Saari D.G.: 1976, ‘On the final evolution of n-body problem’, J. Dif. Eq. 20.
- Saari, D.G.: 1971, 1973, ‘Improbability of collision in Newtonian gravitational system’, (I) Trans. Amer. Math. Soc. 162, 267–271. (II) ibid. 181, 361.
- Saari, D.G.: 1971, ‘Singularities and collision in Newtonian graviational system’, Arch. Rat. Mech. and Anal. 49, 311–320.
- The global solution of the N-body problem
Celestial Mechanics and Dynamical Astronomy
Volume 50, Issue 1 , pp 73-88
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- N-body problem
- blowing up transformation
- analytic continuation
- Industry Sectors
- Wang Qiu-Dong (1)
- Author Affiliations
- 1. Department of Mathematical Science, University of Cincinnati, 45221-0025, Cincinnati, OH, U.S.A