The Schrödinger equation for a Kirchhoff elastic rod with noncircular cross section

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Published under licence by IOP Publishing Ltd
, , Citation Xue Yun et al 2004 Chinese Phys. 13 794 DOI 10.1088/1009-1963/13/6/002

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Author affiliations

1 Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

2 Department of Mechanical Engineering, Shanghai Institute of Technology, Shanghai 200233, China

3 Department of Engineering Mechanics, Shanghai Jiaotong University, Shanghai 200030, China

Dates

  1. Received 27 June 2003
1009-1963/13/6/794

Abstract

The extended Schrödinger equation for the Kirchhoff elastic rod with noncircular cross section is derived using the concept of complex rigidity. As a mathematical model of supercoiled DNA, the Schrödinger equation for the rod with circular cross section is a special case of the equation derived in this paper. In the twistless case of the rod when the principal axes of the cross section are coincident with the Frenet coordinates of the centreline, the Schrödinger equation is transformed to the Duffing equation. The equilibrium and stability of the twistless rod are discussed and a bifurcation phenomenon is presented.

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