中国物理B ›› 2004, Vol. 13 ›› Issue (6): 794-797.doi: 10.1088/1009-1963/13/6/002

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The Schr?dinger equation for a Kirchhoff elastic rod with noncircular cross section

刘延柱1, 陈立群2, 薛纭3   

  1. (1)Department of Engineering Mechanics, Shanghai Jiaotong University, Shanghai 200030, China; (2)Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; (3)Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; Department of Mechanical Engineering, Shanghai Institute of Technology, Shanghai 200233, China
  • 收稿日期:2003-06-27 修回日期:2003-11-04 出版日期:2004-07-05 发布日期:2005-07-05

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

Xue Yun (薛纭)ab, Liu Yan-Zhu (刘延柱)c, Chen Li-Qun (陈立群)a   

  1. a Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; b Department of Mechanical Engineering, Shanghai Institute of Technology, Shanghai 200233, China; c Department of Engineering Mechanics, Shanghai Jiaotong University, Shanghai 200030, China
  • Received:2003-06-27 Revised:2003-11-04 Online:2004-07-05 Published:2005-07-05

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摘要： The extended Schr?dinger 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 Schr?dinger 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 Schr?dinger equation is transformed to the Duffing equation. The equilibrium and stability of the twistless rod are discussed, and a bifurcation phenomenon is presented.

关键词: Kirchhoff elastic rod, Schr?dinger equation, DNA model

Abstract: The extended Schr?dinger 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 Schr?dinger 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 Schr?dinger equation is transformed to the Duffing equation. The equilibrium and stability of the twistless rod are discussed, and a bifurcation phenomenon is presented.

Key words: Kirchhoff elastic rod, Schr?dinger equation, DNA model

中图分类号:  (General theory of classical mechanics of discrete systems)

  • 45.05.+x
46.25.-y (Static elasticity)