The Extended Delaunay Method Applied to First Order Resonance

This paper is concerned with the extended Delaunay method as well as the method of integration of the equations, applied to first order resonance. The equations of the transformation of the extended Delaunay method are analyzed in the (p + 1)/p type resonance in order to build formal, analytical solutions for the resonant problem with more than one degree of freedom. With this it is possible to gain a better insight into the method, opening the possibility for more generalized applications. A first order resonance in the first approximation is carried out, giving a better comprehension of the method, including showing how to eliminate the ‘Poincaré singularity’ in the higher orders.