Contents

This paper explores pattern evocation and the visualization of orbits of the double spherical pendulum. Pattern evocation is a phenomenon where patterns emerge when the �ow of a dy� namical system is viewed in a frame that rotates relative to the inertial frame. The paper begins with a summary of the theory on pattern evocation for mechanical systems with symmetry. The result of this theory is that if the motion in the reduced space is periodic �respectively � quasiperi� odic or almost periodic� � then when viewed in a suitably chosen rotating frame with constant velocity � the motion in the unreduced space is periodic �respectively � quasiperiodic or almost periodic�. The motion of the system viewed in this rotating frame may have a particular pattern or symmetry. Examples of this theory are demonstrated for the double spherical pendulum. A di�erential�algebraic model is created for the double spherical pendulum and is integrated with the simulation package MEXX as well as a custom energy�momentum integrator. � Research partially supported by NSF � DOE � and NATO