Linearized equations of motion in multibody dynamics
(2014) In Mathematics and Mechanics of Solids 21(4). p.454-505- Abstract
In this paper the linearized equations of motion in multibody dynamics are derived. Explicit expressions for the coefficient matrices are presented and given their physical interpretations. The equations of motion are presented in terms of the mechanical stiffness, its adjoint and the associated differential operators. It is demonstrated how the adjoint matrix may be used to find solutions to the associated algebraic eigenvalue problem. The case of multiple roots of the characteristic equation will result in a generalized eigenvalue problem involving the notion of a Jordan chain. Qualitative properties of the spectrum are derived without explicitly solving the characteristic equation. Finally, the mechanical admittance and its spectral... (More)
In this paper the linearized equations of motion in multibody dynamics are derived. Explicit expressions for the coefficient matrices are presented and given their physical interpretations. The equations of motion are presented in terms of the mechanical stiffness, its adjoint and the associated differential operators. It is demonstrated how the adjoint matrix may be used to find solutions to the associated algebraic eigenvalue problem. The case of multiple roots of the characteristic equation will result in a generalized eigenvalue problem involving the notion of a Jordan chain. Qualitative properties of the spectrum are derived without explicitly solving the characteristic equation. Finally, the mechanical admittance and its spectral representations are discussed.
(Less)
- author
- Lidström, P. LU
- organization
- publishing date
- 2014
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- generalized eigenvalue problem, linearized equations, Multibody dynamics, multiple roots, vibrations
- in
- Mathematics and Mechanics of Solids
- volume
- 21
- issue
- 4
- pages
- 52 pages
- publisher
- SAGE Publications
- external identifiers
-
- scopus:84962359828
- wos:000373604900005
- ISSN
- 1081-2865
- DOI
- 10.1177/1081286514526215
- language
- English
- LU publication?
- yes
- id
- 766471be-e31a-4d77-8771-a29302c9761a
- date added to LUP
- 2016-09-26 11:06:11
- date last changed
- 2025-01-12 12:08:17
@article{766471be-e31a-4d77-8771-a29302c9761a,
abstract = {{<p>In this paper the linearized equations of motion in multibody dynamics are derived. Explicit expressions for the coefficient matrices are presented and given their physical interpretations. The equations of motion are presented in terms of the mechanical stiffness, its adjoint and the associated differential operators. It is demonstrated how the adjoint matrix may be used to find solutions to the associated algebraic eigenvalue problem. The case of multiple roots of the characteristic equation will result in a generalized eigenvalue problem involving the notion of a Jordan chain. Qualitative properties of the spectrum are derived without explicitly solving the characteristic equation. Finally, the mechanical admittance and its spectral representations are discussed.</p>}},
author = {{Lidström, P.}},
issn = {{1081-2865}},
keywords = {{generalized eigenvalue problem; linearized equations; Multibody dynamics; multiple roots; vibrations}},
language = {{eng}},
number = {{4}},
pages = {{454--505}},
publisher = {{SAGE Publications}},
series = {{Mathematics and Mechanics of Solids}},
title = {{Linearized equations of motion in multibody dynamics}},
url = {{http://dx.doi.org/10.1177/1081286514526215}},
doi = {{10.1177/1081286514526215}},
volume = {{21}},
year = {{2014}},
}