Dynamical Systems/Mathematical Problems in Mechanics
Stability of relative equilibria and Morse index of central configurations

Presented by: Jean-Baptiste Leblond

Hu, Xijun1; Sun, Shanzhong2
1 Department of Mathematics, Shandong University, Jinan, Shandong, 250100, People's Republic of China
2 Department of Mathematics, Capital Normal University, Beijing, 100048, People's Republic of China
Comptes Rendus. Mathématique, Volume 347 (2009) no. 21-22, pp. 1309-1312.

For the planar n-body problem, if the Morse index or the nullity of a central configuration as a critical point of Newton potential function restricted on the “shape sphere” is odd, then the relative equilibrium corresponding to the central configuration is linearly unstable.

Dans le problème plan des n corps, si l'indice de Morse ou la nullité d'une configuration centrale vue comme un point critique du potentiel newtonien restreint à la « sphère des formes » est impair, l'équilibre relatif correspondant est linéairement instable.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2009.09.023
Hu, Xijun 1; Sun, Shanzhong 2

1 Department of Mathematics, Shandong University, Jinan, Shandong, 250100, People's Republic of China
2 Department of Mathematics, Capital Normal University, Beijing, 100048, People's Republic of China 
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Hu, Xijun; Sun, Shanzhong. Stability of relative equilibria and Morse index of central configurations. Comptes Rendus. Mathématique, Volume 347 (2009) no. 21-22, pp. 1309-1312. doi : 10.1016/j.crma.2009.09.023. http://www.numdam.org/articles/10.1016/j.crma.2009.09.023/

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