Physics
Scientific paper
Mar 1976
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976cemec..13..229g&link_type=abstract
Celestial Mechanics, vol. 13, Mar. 1976, p. 229-246.
Physics
21
Celestial Mechanics, Hamiltonian Functions, Libration, Orbital Mechanics, Algorithms, Asteroids, Boundary Value Problems, Canonical Forms, Degrees Of Freedom, Periodic Functions, Perturbation Theory, Trojan Orbits
Scientific paper
It is shown analytically that many problems of libration in celestial mechanics can be reduced to a perturbation of one degree of freedom defined by a certain intermediate Hamiltonian. This generalization of the ideal resonance problem, in which the term sine-squared x is replaced by a periodic function f(x), is solved to the order of mu-squared using an algorithm which is essentially the same as that employed in the original formulation of the problem. The solution is found to contain a term involving the inversion of an hyperelliptic integral evaluated by quadrature. The results indicate that libration may be simple or multiple, depending on the initial conditions and the nature of the function f(x). Double libration is illustrated with the example of the Trojan asteroid orbits.
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