Astronomy and Astrophysics – Astrophysics
Scientific paper
Jul 1987
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987ap%26ss.135..253d&link_type=abstract
Astrophysics and Space Science (ISSN 0004-640X), vol. 135, no. 2, July 1987, p. 253-260.
Astronomy and Astrophysics
Astrophysics
1
Charge Distribution, Circular Orbits, Euler-Lagrange Equation, Three Body Problem, Angular Velocity, Center Of Mass, Equations Of Motion, Newton Second Law
Scientific paper
A generalization of the classical restricted circular three-body problem is presented, and the existance and location of colinear and equilateral Lagrangian points or solutions are discussed and interpreted. The defined quintic equation is found to have only one real root on the x-axis in the range of x between 1 - mu and infinity if mu is greater than q, and in the range of x between negative infinity and -mu if q is greater than mu. In the range of x between -mu and 1 - mu it is shown to have two, or one double, or no real root on the x-axis with respect to mu greater than q or q greater than mu. In addition, no equilateral solutions are found.
Dionysiou Demetrious D.
Vaiopoulos D. A.
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