A new approach to the planetary theory is examined under the following procedure: 1) we use a canonical perturbation method based on the averaging principle; 2) we adopt Charlier's canonical relative coordinates fixed to the Sun, and the equations of motion of planets can be written in the canonical form; 3) we adopt some devices concerning the development of the disturbing function. Our development can be applied formally in the case of nearly intersecting orbits as the Neptune-Pluto system. Procedure 1) has been adopted by Message (1976).
A canonical perturbation method based on Hamilton-Jacobi theory, used together with Galerkin’s method, is employed to analyze the nonlinearly coupled transverse free oscillations of columns subjected to a constant end force. Integrals of motion, readily obtained from this type of analysis, are used to allow the analytical determination of the main characteristics of the resonant motion and of the region of resonance of the system.
New Approach to the Planetary Theory
