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<td rowspan="2" class="MPReader_Profiles_SpringerLink_Content_PrimitiveHeadingControlCoverImage"><img alt="On the use of linear graph theory in multibody system dynamics" src="/content/102972/cover-medium.jpg" width="95" height="128" /></td><td><h2 class="MPReader_Profiles_SpringerLink_Content_PrimitiveHeadingControlName">
On the use of linear graph theory in multibody system dynamics
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<td class="labelName">Journal</td><td class="labelValue"><a href="/content/102972/?p=5fa8e5a97fd742fda943635f0096b34e&pi=0">Nonlinear Dynamics</a></td>
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<td class="labelName">Publisher</td><td class="labelValue">Springer Netherlands</td>
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<td class="labelName">ISSN</td><td class="labelValue">0924-090X (Print) 1573-269X (Online)</td>
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<td class="labelName">Issue</td><td class="labelValue"><a href="/content/l70t22k19r71/?p=5fa8e5a97fd742fda943635f0096b34e&pi=0">Volume 9, Numbers 1-2 / February, 1996</a></td>
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<td class="labelName">DOI</td><td class="labelValue">10.1007/BF01833294</td>
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<td class="labelName">Pages</td><td class="labelValue">73-90</td>
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<td class="labelName">Subject Collection</td><td class="labelValue"><a href="/engineering/">Engineering</a></td>
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<td class="labelName">SpringerLink Date</td><td class="labelValue">Thursday, July 07, 2005</td>
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<p></p><div class="Heading1"><a name="title"></a>On the use of linear graph theory in multibody system dynamics</div><p class="AuthorGroup">J. J. McPhee<sup>1</sup></p><table><tbody><tr valign="top"><td><span class="Affiliation"><a name="Aff1"></a>(1) </span></td><td><span class="Affiliation">Systems Design Engineering, University of Waterloo, N2L 3G1 Ontario, Canada</span></td></tr></tbody></table><p class="Affiliation"><strong>Received: </strong>26 August 1994 <strong>Accepted: </strong>19 September 1994 </p><div class="Abstract"><a name="Abs1"></a><span class="AbstractHeading">Abstract </span>Multibody dynamics involves the generation and solution of the equations of motion for a system of connected material bodies. The subject of this paper is the use of graph-theoretical methods to represent multibody system topologies and to formulate the desired set of motion equations; a discussion of the methods available for solving these differential-algebraic equations is beyond the scope of this work. After a brief introduction to the topic, a review of linear graphs and their associated topological arrays is presented, followed in turn by the use of these matrices in generating various graph-theoretic equations. The appearance of linear graph theory in a number of existing multibody formulations is then discussed, distinguishing between approaches that use absolute (Cartesian) coordinates and those that employ relative (joint) coordinates. These formulations are then contrasted with formal graph-theoretic approaches, in which both the kinematic and dynamic equations are automatically generated from a single linear graph representation of the system. The paper concludes with a summary of results and suggestions for further research on the graph-theoretical modelling of mechanical systems.</div><p class="Keyword"><span class="KeywordHeading">Key words </span>Multibody dynamics - linear graph theory - absolute and joint coordinates</p><hr>
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<p></p><h2><a name="Bib1"></a>References</h2>
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<td><a name="CR28"></a>Lai, H. J., Haug, E. J., Kim, S. S., and Bae, D. S., <img src="/content/p64768w654438463/xlarge8216.gif" alt="lsquo" align="BASELINE" BORDER="0">A decoupled flexible-relative co-ordinate recursive approach for flexible multibody dynamics<img src="/content/p64768w654438463/xlarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0">,<i>International Journal for Numerical Methods in Engineering</i>
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<td> </td>
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<tr valign="top">
<td>29.</td>
<td><a name="CR29"></a>Andrews, G. C. and Kesavan, H. K., <img src="/content/p64768w654438463/xlarge8216.gif" alt="lsquo" align="BASELINE" BORDER="0">The vector-network model: A new approach to vector dynamics<img src="/content/p64768w654438463/xlarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0">,<i>Mechanisms and Machine Theory</i>
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</tr>
<tr>
<td> </td>
</tr>
<tr valign="top">
<td>30.</td>
<td><a name="CR30"></a>Andrews, G. C., Richard, M. J., and Anderson, R. J., <img src="/content/p64768w654438463/xlarge8216.gif" alt="lsquo" align="BASELINE" BORDER="0">A general vector-network formulation for dynamic systems with kinematic constraints<img src="/content/p64768w654438463/xlarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0">,<i>Mechanism and Machine Theory</i>
<b>23</b>, 1988, 243–256.<br><a href="http://dx.doi.org.ezproxy.lib.utexas.edu/10.1016/0094-114X(88)90109-7" target="_blank"><img src="/images/crossref_link.gif" border="0" alt="CrossRef" width="65" height="20"></a></td>
</tr>
<tr>
<td> </td>
</tr>
<tr valign="top">
<td>31.</td>
<td><a name="CR31"></a>McPhee, J. J., <img src="/content/p64768w654438463/xlarge8216.gif" alt="lsquo" align="BASELINE" BORDER="0">Formulation of multibody dynamics equations in absolute or relative coordinates using the vector-network method<img src="/content/p64768w654438463/xlarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0">,<i>Machine Elements and Machine Dynamics</i>, ASME DE-Vol. 71, September 1994, pp. 361–368.</td>
</tr>
<tr>
<td> </td>
</tr>
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