# Accession Number:

## AD0645544

# Title:

## DOUBLY SYMMETRIC ORBITS ABOUT THE COLLINEAR LAGRANGIAN POINTS,

# Descriptive Note:

# Corporate Author:

## BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB

# Personal Author(s):

# Report Date:

## 1966-10-01

# Pagination or Media Count:

## 48.0

# Abstract:

The forms and stability of three families of periodic solutions in the three-dimensional case of the Restricted Problem are discussed using the two-point boundary value theory and computing the eigenvalues of the Jacobians of the solutions. It is found that stable members of low inclinations in the case of L2 and L3 indeed exist. The question of a possible new integral in the neighborhood of these points is discussed, together with the equivalent case of galactic motions. It is concluded that a new integral with a single-valued gradient cannot exist unless its gradient is collinear to the gradient of the energy integral along all singular closed solutions. Ordinary solutions, on the other hand, are never found after extensive research by many investigators and thus the above conclusion seems to be general. Author

# Descriptors:

# Subject Categories:

- Celestial Mechanics
- Theoretical Mathematics