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Technical Brief

A Detailed Derivation of the Velocity-Dependent Inertia Forces in the Floating Frame of Reference Formulation

[+] Author and Article Information
Karim Sherif

Johannes Kepler University of Linz,
Altenbergerstr. 69,
Linz 4040, Austria
e-mail: karim.sherif@jku.at

Karin Nachbagauer

Faculty of Engineering and Environmental Sciences,
University of Applied Sciences Upper Austria,
Stelzhamerstr. 23,
Wels 4600, Austria
e-mail: karin.nachbagauer@fh-wels.at

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received June 24, 2013; final manuscript received November 21, 2013; published online July 11, 2014. Assoc. Editor: Javier Cuadrado.

J. Comput. Nonlinear Dynam 9(4), 044501 (Jul 11, 2014) (8 pages) Paper No: CND-13-1155; doi: 10.1115/1.4026083 History: Received June 24, 2013; Revised November 21, 2013

In the case of complex multibody systems, an efficient and time-saving computation of the equations of motion is essential; in particular, concerning the inertia forces. When using the floating frame of reference formulation for modeling a multibody system, the inertia forces, which include velocity-dependent forces, depend nonlinearly on the system state and, therefore, have to be updated in each time step of the dynamic simulation. Since the emphasis of the present investigation is on the efficient computation of the velocity-dependent inertia forces as along with a fast simulation of multibody systems, a detailed derivation of the latter forces for the case of a general rotational parameterization is given. It has to be emphasized that the present investigations revealed a simpler representation of the velocity-dependent inertia forces compared to results presented in the literature. In contrast to the formulas presented in the literature, the presented formulas do not depend on the type of utilized rotational parameterization or on any associated assumptions.

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