A transverse spinning double pendulum

A transverse spinning double pendulum is introduced. This pendulum is of in terest as a simple mechanical system with two degrees of freedom with rotat ion which is autonomous. In addition to having physical origins, the pendul um is constructable for experimental observation. Our main interest in intr oducing and analyzing this system is that it is the simplest physical syste m with the codimension two singularity - in the linearization about the tri vial solution - associated with coalescence of four zero eigenvalues. It is the dynamics of the nonlinear system in the neighbourhood of this singular ity that is of interest. We study this problem using normal form theory. An algorithm for the Cushman-Sanders normal form is constructed and analyzed. A representative model for the truncated normal form is presented. This tr uncated normal form has seven parameters; it is not integrable in general a nd it is predicted that the dynamics associated with this model will be qui te complex. (C) 2000 Elsevier Science Ltd. All rights reserved.