Development of Symbolic Computation Methods for Nonlinear Dynamics

摘要

Under the supervision of principal investigator R.H. Rand, software has been written in MACSYMA which automatically performs normal form computations for systems of nonlinear nonautonomous differential equations. We have produced a package which permits the user to perform Taylor expanded near identity transformations with unevaluated coefficients on a system of autonomous ODE's (valid to terms of arbitrary order), and then to choose the transformation coefficients so that the resulting system is in normal form. This work has been applied to the nonlinear parametric stiffness control of flexible systems by Professors Moon and Rand, and to the dynamics of coupled van der Pol oscillators.