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Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (9): 1193-1200.doi: https://doi.org/10.1007/s10483-009-0914-x

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Generalized elastic curves in the Lorentz flat space L4

黄荣培 商东虎   

  1. Department of Mathematics, East China Normal University, Shanghai 200241, P. R. China
  • 收稿日期:2009-03-23 修回日期:2009-07-03 出版日期:2009-09-01 发布日期:2009-09-01

Generalized elastic curves in the Lorentz flat space L4

 HUANG Rong-Pei, SHANG Dong-Hu   

  1. Department of Mathematics, East China Normal University, Shanghai 200241, P. R. China
  • Received:2009-03-23 Revised:2009-07-03 Online:2009-09-01 Published:2009-09-01

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摘要： In this paper, we study the extremals of the curvature energy actions on non-null curves in the four-dimensional Lorentz-Minkowski space. We derive the motion equations and find three Killing fields along the generalized elastic curves. We also construct a cylindrical coordinate system using these Killing fields and express the generalized elastic curves by means of quadratures.

关键词: generalized elastic curve, geometrical particle model, Killing field, Lorentz-Minkowski space

Abstract: In this paper, we study the extremals of the curvature energy actions on non-null curves in the four-dimensional Lorentz-Minkowski space. We derive the motion equations and find three Killing fields along the generalized elastic curves. We also construct a cylindrical coordinate system using these Killing fields and express the generalized elastic curves by means of quadratures.

Key words: generalized elastic curve, geometrical particle model, Killing field, Lorentz-Minkowski space

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