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Partial decomposition of nonlinear Euler–Lagrange equations with a state transform

Michiel De Roeck (UGent) , Jasper Juchem (UGent) , Guillaume Crevecoeur (UGent) and Mia Loccufier (UGent)
(2024) NONLINEAR DYNAMICS. 112(1). p.15-22
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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.
Keywords
Electrical and Electronic Engineering, Applied Mathematics, Mechanical Engineering, Ocean Engineering, Aerospace Engineering, Control and Systems Engineering, Euler-Lagrange, Decoupling, State transform, Matrix decomposition

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MLA
De Roeck, Michiel, et al. “Partial Decomposition of Nonlinear Euler–Lagrange Equations with a State Transform.” NONLINEAR DYNAMICS, vol. 112, no. 1, 2024, pp. 15–22, doi:10.1007/s11071-023-09004-6.
APA
De Roeck, M., Juchem, J., Crevecoeur, G., & Loccufier, M. (2024). Partial decomposition of nonlinear Euler–Lagrange equations with a state transform. NONLINEAR DYNAMICS, 112(1), 15–22. https://doi.org/10.1007/s11071-023-09004-6
Chicago author-date
De Roeck, Michiel, Jasper Juchem, Guillaume Crevecoeur, and Mia Loccufier. 2024. “Partial Decomposition of Nonlinear Euler–Lagrange Equations with a State Transform.” NONLINEAR DYNAMICS 112 (1): 15–22. https://doi.org/10.1007/s11071-023-09004-6.
Chicago author-date (all authors)
De Roeck, Michiel, Jasper Juchem, Guillaume Crevecoeur, and Mia Loccufier. 2024. “Partial Decomposition of Nonlinear Euler–Lagrange Equations with a State Transform.” NONLINEAR DYNAMICS 112 (1): 15–22. doi:10.1007/s11071-023-09004-6.
Vancouver
1.
De Roeck M, Juchem J, Crevecoeur G, Loccufier M. Partial decomposition of nonlinear Euler–Lagrange equations with a state transform. NONLINEAR DYNAMICS. 2024;112(1):15–22.
IEEE
[1]
M. De Roeck, J. Juchem, G. Crevecoeur, and M. Loccufier, “Partial decomposition of nonlinear Euler–Lagrange equations with a state transform,” NONLINEAR DYNAMICS, vol. 112, no. 1, pp. 15–22, 2024.
@article{01HGDNV08GPP968DPSS2VWWP4Y,
  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.}},
  author       = {{De Roeck, Michiel and Juchem, Jasper and Crevecoeur, Guillaume and Loccufier, Mia}},
  issn         = {{0924-090X}},
  journal      = {{NONLINEAR DYNAMICS}},
  keywords     = {{Electrical and Electronic Engineering,Applied Mathematics,Mechanical Engineering,Ocean Engineering,Aerospace Engineering,Control and Systems Engineering,Euler-Lagrange,Decoupling,State transform,Matrix decomposition}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{15--22}},
  title        = {{Partial decomposition of nonlinear Euler–Lagrange equations with a state transform}},
  url          = {{http://doi.org/10.1007/s11071-023-09004-6}},
  volume       = {{112}},
  year         = {{2024}},
}
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