Study of the Double Mathematical Pendulum — III. Melnikov's Method Applied to the System In the Limit of Small Ratio of Pendulums Masses

We consider the double mathematical pendulum in the limit when the ratio of pendulums masses is close to zero and if the value of one of other system parameters is close to degenerate value (i.e. zero or infinity). We investigate homoclinic intersections, using Melnikov's method, and obtain an asymptotic formula for the homoclinic invariant in this case.