High-Order Lie Derivatives from Taylor Series in the ADTAYL Package

Nedialko S. Nedialkov; John D. Pryce

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arXiv · 2601.10828

High-Order Lie Derivatives from Taylor Series in the ADTAYL Package

Nedialko S. Nedialkov·John D. Pryce

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Abstract

High-order Lie derivatives are essential in nonlinear systems analysis. If done symbolically, their evaluation becomes increasingly expensive as the order increases. We present a compact and efficient numerical approach for computing Lie derivatives of scalar, vector, and covector fields using the MATLAB ADTAYL package. The method exploits a fact noted by R\"obenack: that these derivatives coincide, up to factorial scaling, with the Taylor coefficients of expressions built from a Taylor expansion about a trajectory point and, when required, the associated variational matrix. Computational results for a gantry crane model demonstrate orders of magnitude speedups over symbolic evaluation using the MATLAB Symbolic Math Toolbox.

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Nedialko S. Nedialkov, John D. Pryce. 2026-01-15. High-Order Lie Derivatives from Taylor Series in the ADTAYL Package. https://arxiv.org/abs/2601.10828

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