Conformal Invariance and Conserved Quantities for Lagrange Equation of Thin Elastic Rod

Abstract

Basing on the analytical mechanics methods, the Lagrangian equations of thin elastic rod is constructed. The definition of conformal invariance for the Lagrange mechanics of elastic rod is given. The criterions that conformal invariance of elastic rod is the Lie symmetry are obtained based on the Lie point transformation group. The structure equation and conserved quantity deduced from conformal invariance of elastic rod are constructed. Take twist rod as an example to illustrate the application of the results got in this paper.

Growth induced buckling of morphoelastic rod in viscous medium*

“…Wang et al studied symmetries and conserved quantities of Kirchhoff and Cosserat elastic rods. [21][22][23] Since many living things such as cell, sperm, and DNA are in fluid environment, viscous action should be taken into consideration in research of their mechanical behavior. Wolgemuth et al [8] studied dynamic supercoiling bifurcation of Bacillus subtilis in fluid using the filament model to explain complex supercoiled structures during cells growth.…”