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Screw and Lie group theory in multibody dynamics
AuthorMüller, Andreas
Published in
Multibody System Dynamics, 2018, Vol. 42, Issue 2, page 219-248
PublishedSpringer Netherlands, 2018
Document typeJournal Article
Keywords (EN)Multibody system dynamics / Relative coordinates / Recursive algorithms / O(n) / Screws Lie groups / NewtonEuler equations / Lagrange equations / Kanes equations / EulerJourdain equations / Projection equations / Lie group integration / Linearization
URNurn:nbn:at:at-ubl:3-1757 Persistent Identifier (URN)
 The work is publicly available
Screw and Lie group theory in multibody dynamics [0.93 mb]
Abstract (English)

Screw and Lie group theory allows for user-friendly modeling of multibody systems (MBS), and at the same they give rise to computationally efficient recursive algorithms. The inherent frame invariance of such formulations allows to use arbitrary reference frames within the kinematics modeling (rather than obeying modeling conventions such as the DenavitHartenberg convention) and to avoid introduction of joint frames. The computational efficiency is owed to a representation of twists, accelerations, and wrenches that minimizes the computational effort. This can be directly carried over to dynamics formulations. In this paper, recursive O(n) NewtonEuler algorithms are derived for the four most frequently used representations of twists, and their specific features are discussed. These formulations are related to the corresponding algorithms that were presented in the literature. Two forms of MBS motion equations are derived in closed form using the Lie group formulation: the so-called EulerJourdain or “projection” equations, of which Kanes equations are a special case, and the Lagrange equations. The recursive kinematics formulations are readily extended to higher orders in order to compute derivatives of the motions equations. To this end, recursive formulations for the acceleration and jerk are derived. It is briefly discussed how this can be employed for derivation of the linearized motion equations and their time derivatives. The geometric modeling allows for direct application of Lie group integration methods, which is briefly discussed.

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