Another Multibody Dynamics in Natural Coordinates through Automatic Differentiation and High-Index DAE Solving

Authors

DOI:

https://doi.org/10.14232/actacyb.24.3.2020.4

Keywords:

Lagrangian mechanics, differential-algebraic equations, natural coordinates, simulation, algorithmic differentiation, YAML

Abstract

The Natural Coordinates (NCs) method for Lagrangian modelling and simulation of multi-body systems is valued for giving simple, sparse models. We describe our version of it (NPNCs) and compare with the classical ap- proach of Jalón and Bayo (JBNCs). NPNCs use the high-index differential- algebraic equation solver DAETS. Algorithmic differentiation, not symbolic algebra, forms the equations of motion from the Lagrangian. NPNCs give significantly smaller equation systems than JBNCs, at the cost of a non- constant mass matrix for fully 3D models—a minor downside in the DAETS context. A 2D and a 3D example are presented, with numerical results.

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Author Biography

Nedialko Nedialkov, McMaster University

Professor, Department of Computing and Software

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Published

2020-03-16

How to Cite

Pryce, J. D., & Nedialkov, N. (2020). Another Multibody Dynamics in Natural Coordinates through Automatic Differentiation and High-Index DAE Solving. Acta Cybernetica, 24(3), 315–341. https://doi.org/10.14232/actacyb.24.3.2020.4

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Section

Uncertainty Modeling, Software, Verified Computing and Optimization