ROUTH'S CRITICAL MASS RATIO AT THE TRIANGULAR LIBRATION CENTERS.
Abstract
Routh's criterion concerning the existence of periodic solutions around the triangular libration centers is shown to be valid only at the first order. For mass ratios greater than Routh's critical value, the analytical relations between the mass ratio and the lower bound of the orbital parameter is expanded in power series up to the fourteenth order. The corresponding d'Alembert series representing the limiting periodic orbits up to the same order are used to provide approximate initial conditions for a numerical integration method. For mass ratios as high as 0.044 (in canonical units), the Jacobi constant of the limiting orbits is a slightly increasing function of the mass ratio; their characteristic exponents are of the stable type. As the mass goes on increasing, the multipliers keep moving on the unit circle in the complex plane from the real unit point to its opposite. The orbits evolve from infinitesimal ellipses centered at L sub 4 into large size asymmetrical ovals around that point. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1965
- Accession Number
- AD0621575
Entities
People
- Andre Deprit
Organizations
- Boeing