Proof of the stability of Lagrangian solutions at a critical relation of masses.
Abstract
The Lagrangian solutions of the plane circular restricted threebody problem will be stable if the chief gravitating bodies have a critical mass ratio. A proof is obtained by demonstrating the Lyapunov stability of the equilibrium position of a selfcontained Hamiltonian system with two degrees of freedom, provided the frequencies of the linear system are equal (secondorder resonance) and the defining matrix has nonsimple elementary divisors.
 Publication:

Pisma v Astronomicheskii Zhurnal
 Pub Date:
 April 1978
 Bibcode:
 1978PAZh....4..148S
 Keywords:

 Dynamic Stability;
 EulerLagrange Equation;
 Liapunov Functions;
 Mass Ratios;
 Numerical Stability;
 Three Body Problem;
 Canonical Forms;
 Critical Mass;
 Differential Equations;
 HamiltonJacobi Equation;
 Linear Systems;
 Resonant Frequencies;
 Astronomy;
 ThreeBody Problem:Restricted;
 ThreeBody Problem: Stability