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This paper provides a detailed introduction into the differential algebra(DA) based normal form algorithm using the example of the symplectic onedimensional system of the centrifugal governor. The intention of this paper isto make the single steps of the algorithm as transparent as possible in thehope that the understanding and use of DA normal form methods will spreadthroughout the scientific community.

Introduction to the Differential Algebra Normal Form Algorithm using the Centrifugal Governor as an Example