Open Access
Translator Disclaimer
2013 The Characterization of the Variational Minimizers for Spatial Restricted N + 1 -Body Problems
Fengying Li, Shiqing Zhang, Xiaoxiao Zhao
Abstr. Appl. Anal. 2013(SI44): 1-5 (2013). DOI: 10.1155/2013/845795

Abstract

We use Jacobi's necessary condition for the variational minimizer to study the periodic solution for spatial restricted N + 1 -body problems with a zero mass on the vertical axis of the plane for N equal masses. We prove that the minimizer of the Lagrangian action on the anti-T/2 or odd symmetric loop space must be a nonconstant periodic solution for any 2 N 472 ; hence the zero mass must oscillate, so that it cannot be always in the same plane with the other bodies. This result contradicts with our intuition that the small mass should always be at the origin.

Citation

Download Citation

Fengying Li. Shiqing Zhang. Xiaoxiao Zhao. "The Characterization of the Variational Minimizers for Spatial Restricted N + 1 -Body Problems." Abstr. Appl. Anal. 2013 (SI44) 1 - 5, 2013. https://doi.org/10.1155/2013/845795

Information

Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1331.70030
MathSciNet: MR3064349
Digital Object Identifier: 10.1155/2013/845795

Rights: Copyright © 2013 Hindawi

JOURNAL ARTICLE
5 PAGES


SHARE
Vol.2013 • No. SI44 • 2013
Back to Top