98-544 Ivanov A.V.

Study of the double mathematical pendulum - I. Numerical investigation of homoclinic transversal intersections (2589K, LATeX) Jul 29, 98

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Abstract. We study numerically the double mathematical pendulum in terms of the Poincar\'e section. Approximate positions of some hyperbolic periodic points are obtained visually from the pictures of the phase portrait, and their precise coordinates are calculated by use of the Newton method. The pictures of the corresponding stable and unstable manifolds are drawn, the positions of some homoclinic points are found numerically, and their homoclinic invariants are calculated. This is done for 3 chosen sets of system parameters and values of the energy. The nonnullity of the mentioned homoclinic invariants implies the nonintegrability of the system for these values of the parameters and energy. It means that the related Poincar\'e map has no a first integral on that energy level.

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