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DeLaunay's reduced Hamiltonian of the main problem in lunar theory is checked against a new analytical theory based on Lie transforms. It is found to be correct up to order 9 with the exception of one error in addition of order 7.
Poisson series of three variables are manageable symbolically through a set of formal subroutines written partially in the IBM 7094 machine language, but to be called in the FORTRAN language for use in FORTRAN programs. An effort has been made to supply those operations which are most required by Celestial Mechanics. The routines are entirely self-contained… (More)
For an integrable dynamical system with one degree of freedom, "painting" the integral over the phase space proves to be very effective for uncovering the global flow down to minute details. Applied to the main problem in artificial satellite theory, for instance, the technique reveals an intricate configuration of equilibria and bifurcations when the polar… (More)
A massively parallel processor proves to be a powerful tool for manipulating the very large Poisson series encountered in non-linear dynamics. Exploiting the algebraic structure of Poisson series leads quite naturally to parallel data structures and algorithms for symbolic manipulation. Exercising the parallel symbolic processor on the solution of Kepler's… (More)