| FUNDAMENTAL AREAS OF PHENOMENOLOGY(INCLUDING APPLICATIONS) |
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Jourdain Principle of a Super-Thin Elastic Rod Dynamics |
| XUE Yun, SHANG Hui-Lin |
| School of Mechanical and Automation Engineering, Shanghai Institute of Technology, Shanghai 200235 |
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| Cite this article: |
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XUE Yun, SHANG Hui-Lin 2009 Chin. Phys. Lett. 26 074501 |
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Abstract A super thin elastic rod is modeled with a background of DNA super coiling structure, and its dynamics is discussed based on the Jourdain variation. The cross section of the rod is taken as the object of this study and two velocity spaces about arc coordinate and the time are obtained respectively. Virtual displacements of the section on the two velocity spaces are defined and can be expressed in terms of Jourdain variation. Jourdain principles of a super thin elastic rod dynamics on arc coordinate and the time velocity space are established, respectively, which show that there are two ways to realize the constraint conditions. If the constitutive relation of the rod is linear, the Jourdain principle takes the Euler-Lagrange form with generalized oordinates. The Kirchhoff equation, Lagrange equation and Appell equation can be derived from the present Jourdain principle. While the rod subjected to a surface constraint, Lagrange equation with undetermined multipliers may be derived.
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| Keywords:
45.20.Jj
45.90.+t
46.70.Hg
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Received: 19 January 2009
Published: 02 July 2009
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