Ivanov A.V.
Study of the double mathematical pendulum - I.
Numerical investigation of homoclinic transversal intersections
(2589K, LATeX)
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.