Abstract
The Euler–Lagrange (EL) formalism is extensively used to describe a wide range of systems. The choice of the generalised coordinates is not unique and influences the intricacy of the coupling terms between the equations of motion. A coordinate transformation can vastly reduce this complexity, yielding a (partially) decoupled system description. This work proposes a state transform of the original EL equation resulting in an identity inertia matrix. Since the centrifugal and Coriolis terms originate from the derivatives of the inertia (or mass) matrix, the matrix containing these terms is either reduced to a skew-symmetric one or in a limited number of instances reduced to zero. In contrast to prior work, that relied on solving a set of ordinary differential equations, the transformation matrix can be determined using an algebraic equation. As a result, the suggested methodology yields an easy-to-use and powerful tool for reducing and (partially) decoupling any equations of motion expressed in the EL formalism.
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De Roeck, M., Juchem, J., Crevecoeur, G. et al. Partial decomposition of nonlinear Euler–Lagrange equations with a state transform. Nonlinear Dyn 112, 15–22 (2024). https://doi.org/10.1007/s11071-023-09004-6
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DOI: https://doi.org/10.1007/s11071-023-09004-6