Structure properties and Noether symmetries for super-long elastic slender rod

DNA is a nucleic acid molecule with double-helical structures thatare special symmetrical structures attracting great attention ofnumerous researchers. The super-long elastic slender rod, animportant structural model of DNA and other long-train molecules, isa useful tool in analysing the symmetrical properties and thestabilities of DNA. This paper studies the structural properties of asuper-long elastic slender rod as a structural model of DNA by usingKirchhoff's analogue technique and presents the Noether symmetries ofthe model by using the method of infinitesimal transformation. Basedon Kirchhoff's analogue it analyses the generalized Hamiltoncanonical equations. The infinitesimal transformations with respectto the radial coordinate, the generalized coordinates, and thequasi-momenta of the model are introduced. The Noether symmetries andconserved quantities of the model are obtained.