Formulation of Kirchhoff Rod Based on Quasi-coordinates

Authors

  • Y. Z. Liu
  • Y. Xue

Abstract

The quasi-coordinates are applied to formulate Kirchhoff's rod. The potential energy of the rod expressed by the quasi-coordinates has a similar form as the kinetic energy and complementary kinetic energy in dynamics. The conjugate quasi-momentum is defined and the canonical equations due to the quasi-coordinates are given. Kirchhoff's equations can be derived directly from Boltzman-Hamel's equations or its canonical form with arc length s as independent variables. Lagrange's theorem is extended to determine the stability of equilibrium con-figuration of the elastic rod, and is proved using the Lyapunov's direct method. It is noticed that the condition of stability has a different physical explanation than in dynamics.

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Published

2019-08-07

How to Cite

Liu, Y. Z. and Xue, Y. (2019) “Formulation of Kirchhoff Rod Based on Quasi-coordinates”, Technische Mechanik - European Journal of Engineering Mechanics, 24(3-4), pp. 206–210. Available at: https://journals.ub.ovgu.de/index.php/techmech/article/view/931 (Accessed: 21 November 2024).

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