Proof of the stability of Lagrangian solutions for a critical mass ratio

Details Proof of the stability of Lagrangian solutions for a critical mass ratio Proof of the stability of Lagrangian solutions for a critical mass ratio

Apr 1978

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978pazh....4..148s&link_type=abstract

(Pis'ma v Astronomicheskii Zhurnal, vol. 4, Mar. 1978, p. 148-152.) Soviet Astronomy Letters, vol. 4, Mar.-Apr. 1978, p. 79-81.

Astronomy and Astrophysics

Astronomy

3

Dynamic Stability, Euler-Lagrange Equation, Liapunov Functions, Mass Ratios, Numerical Stability, Three Body Problem, Canonical Forms, Critical Mass, Differential Equations, Hamilton-Jacobi Equation, Linear Systems, Resonant Frequencies

Scientific paper

The Lagrangian solutions of the plane circular restricted three-body 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 self-contained Hamiltonian system with two degrees of freedom, provided the frequencies of the linear system are equal (second-order resonance) and the defining matrix has nonsimple elementary divisors.

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