Normal Form and Center Manifold Calculations on MACSYMA
This paper describes the use of the symbolic manipulation system MACSYMA to facilitate normal form and center manifold computations, which arise in nonlinear dynamics problems. These computations represent a relatively new approach towards obtaining approximate solutions to systems of ordinary differential equations. A near-identity coordinate transformation in the form of a power series is used to locally transform a given system into a normal (i.e., simple or canonical) form. Center manifold calculations are a related technique for reducing the number of dimensions in a given system of ordinary differential equations by restricting attention to the flow on an invariant subspace. A MACSYMA program developed to perform such computations is presented and described in detail. The program is illustrated by applying it to a sample nonlinear dynamics problem.
KeywordsNormal Form Equilibrium Point Invariant Subspace Nonlinear Dynamic Problem Function Decompose
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