Abstract
It is shown here that many problems of libration in celestial mechanics can be reduced to a perturbation of anintermediary defined by the Hamiltonian $$F = B\left( y \right) + 2\mu ^2 A\left( y \right)f\left( x \right).$$ This generalization of the Ideal Resonance Problem, with a periodic functionf(x) replacing sin2 x, is solved here toO(μ 2) by an algorithm that is essentially the same as the one used in the original formulation. The solution is of the formx=x(u), u=u(t), y=y(x), with the functionx(u) commonly involving the inversion of a hyperelliptic integralu(x), evaluated by quadrature. Libration may be simple or multiple, depending on the nature of the functionf(x) and on the initial conditions. Double libration is illustrated here by the horseshoe-shaped orbits enclosing two libration centers.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
