On the coupling of lunisolar resonances for earth satellite orbits

The resonance Cl occurs when the longitude of the perigee measured from the equinox becomes a slow angle in the doubly averaged equations of motion This resonance is one of the 'critical inclination' family with I approximate to 46 degrees. For prograde Earth satellite orbits, up to five critical points can be identified. Only simple pitchfork bifurcations occur for the single resonance Cl. A two degrees of freedom system is studied to check how a coupling of two lunisolar resonances affects the results furnished by the analysis of an isolated resonance case. In the system with two critical angles (g + h and h + 2 lambda (circle dot)), seven types of critical points have been identified. The critical points arise and change their stability through 11 bifurcations. If the initial conditions are selected close to the critical points, the system becomes chaotic as shown in Poincare maps.