Statistics – Computation
Scientific paper
Jul 1985
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985acmec..55..267i&link_type=abstract
Acta Mechanica (ISSN 0001-5970), vol. 55, July 1985, p. 267-272.
Statistics
Computation
Celestial Mechanics, Computational Astrophysics, Euler-Lagrange Equation, Three Body Problem, Nonlinear Equations, Numerical Analysis, Polynomials
Scientific paper
The Lagrange equation is a quintic (fifth-degree) equation appearing in a stationary solution of the three-body problem in celestial mechanics. This equation has one positive root, which is the only required in the above problem. In the present paper, an elementary real integral formula for the closed-form solution of nonlinear equations is applied to the solution of the Lagrange equation. Two different approaches to this solution are described in detail, and numerical results (obtained by both approaches) are displayed. Beyond the Lagrange equation, the present results are also applicable to the solution of other nontrivial quintic and higher-degree polynomial equations.
Ioakimidis N. I.
Papadakis K. E.
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