CONSTRUCTION OF ORBITS ASYMPTOTIC TO A PERIODIC ORBIT,
Abstract
In the immediate neighborhood of an unstable periodic orbit, the families of orbits asymptotic to it may be expanded in power series of an orbital parameter, the coefficients being successive variations of increasing order from the generating orbit. When the dynamical system is Hamiltonian, conservative and with two degrees of freedom, the intrinsic components of these variations are shown to be solutions of a recurrent sequence consisting at each step of a nonhomogeneous Hill's equation for the normal displacements and of a quadrature for the tangential components. Accordingly, Floquet's theory reduces the construction of the asymptotic series to a chain of routine operations, like trigonometric interpolations and elementary primitives. In the case of the restricted problem of three bodies, even the development of the force function about the periodic orbit can be implemented automatically on a computer. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1968
- Accession Number
- AD0670794
Entities
People
- Andre Deprit
- Jacques Henrard
Organizations
- Boeing