High-Order Lie Derivatives from Taylor Series in the ADTAYL Package
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911378842845184 |
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| author | Nedialkov, Nedialko S. Pryce, John D. |
| author_facet | Nedialkov, Nedialko S. Pryce, John D. |
| contents | 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 Röbenack: 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10828 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | High-Order Lie Derivatives from Taylor Series in the ADTAYL Package Nedialkov, Nedialko S. Pryce, John D. Numerical Analysis Mathematical Software 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 Röbenack: 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. |
| title | High-Order Lie Derivatives from Taylor Series in the ADTAYL Package |
| topic | Numerical Analysis Mathematical Software |
| url | https://arxiv.org/abs/2601.10828 |