Computer Algebra as a Tool for Analyzing Nonlinear Systems

摘要: We have studied a variety of weakly perturbed nonlinear dynamical systems using the method normal forms, reduction scheme, introduced by Poincare in late nineteenth century. The was formalized Birkhoff who applied it extensively to Hamiltonian mechanics. By invoking near-identity coordinate transformation, forms converts differential equations into simplified motion for zerothorder approximation true solution [1,2,3]. These transformations, functions zeroth-order approximations, are found solving sequence linear which determined spectrum operator associated with linear, unperturbed motion. algebra related these calculations is intensive and well-suited symbolic programming capabilities Maple. Through use procedures written Maple we performed high-order form computations investigated exploitation an inherent nonuniqueness [4,5]. will show how this can be utilized obtain transformed that tailored needs investigator. Coupled computer algebra, potentially powerful tool examination [6].