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A Comparison Case Study For Dynamics Analysis Methods In Applied Multibody Dynamics

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2006 Annual Conference & Exposition


Chicago, Illinois

Publication Date

June 18, 2006

Start Date

June 18, 2006

End Date

June 21, 2006



Conference Session

Innovative Teaching Techniques in Mechanics

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Page Count


Page Numbers

11.27.1 - 11.27.14



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Paper Authors


Shanzhong (Shawn) Duan South Dakota State University

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Shanzhong (Shawn) Duan received his Ph.D. from Rensselaer Polytechnic Institute in 1999. He has been working as a software engineer at Autodesk for five years before he became an assistant professor at South Dakota State University in 2004. His current research interests include virtual prototyping, mechanical design and CAD/CAE/CAM.

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NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract

A Comparison Case Study for Dynamics Analysis Methods in Applied Multibody Dynamics


This paper discusses how a simple comparison case study has been utilized in an applied multibody dynamics (AMD) course to enhance students’ learning of dynamic analysis methods to set up equations of motion for multibody systems. The comparison case used is a planar rigid body double pendulum with a pin joint connection between two bodies. This simple case has helped students directly understand and see advantages and disadvantages of each dynamic analysis method used to set up equations of motion. Based on what they have learned from this case study, students have a better understanding of targeted dynamic analysis methods and can more efficiently choose a proper method to analyze the motion behaviors of their design applications than they could previously.


An applied multibody dynamics course is usually offered to mechanical engineering undergraduates in their senior year and to graduates in their first year. It is an advanced topic and requires that students have a background in linear algebra, vector-matrix operations, dynamics, numerical analysis, and fundamentals of computer science, as well as in basic programming skills. The specific contents of multibody dynamics may vary from school to school. But generally speaking, they may contain but are not limited to the following: (1) Multibody kinematics: coordinate transformation matrixes and direction cosines, kinematical formulas, partial velocities, partial angular velocities, Euler angles, Euler parameters and kinematical differential equations, and so on; (2) Inertia: rotation of coordinate axes for inertia matrices and principal moments of inertia; (3) Multibody kinetics: various dynamic analysis methods for equations of motion. (4) Numerical issues in applied multibody dynamics6, 11, 12.

In practice, many dynamics analysis methods are available for formulation of equations of motion of a multibody system. Newton-Euler equations, Lagrange’s equations, principles of virtual work, Hamilton’s principle, Gauss’s principle, Jordan’s principle, Kane’s method, and even finite element methods have been used by researchers in various applications1. Three

Duan, S. S. (2006, June), A Comparison Case Study For Dynamics Analysis Methods In Applied Multibody Dynamics Paper presented at 2006 Annual Conference & Exposition, Chicago, Illinois. 10.18260/1-2--1072

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