Noether symmetry and conserved quantities of the analytical dynamics of a Cosserat thin elastic rod

2013 ◽  
Vol 22 (10) ◽  
pp. 104503 ◽  
Author(s):  
Peng Wang ◽  
Yun Xue ◽  
Yu-Lu Liu
Keyword(s):  
Noether Symmetry ◽  
Conserved Quantities ◽  
Analytical Dynamics ◽  
Elastic Rod ◽  
Thin Elastic Rod

scholarly journals Mei symmetries and the Noether conserved quantities of super-thin elastic rod

2009 ◽  
Vol 58 (11) ◽  
pp. 7426
Author(s):  
Cui Jian-Xin ◽  
Gao Hai-Bo ◽  
Hong Wen-Xue
Keyword(s):  
Conserved Quantities ◽  
Elastic Rod ◽  
Thin Elastic Rod

Mei symmetry and conserved quantities in Kirchhoff thin elastic rod statics

2012 ◽  
Vol 21 (7) ◽  
pp. 070203 ◽  
Author(s):  
Peng Wang ◽  
Yun Xue ◽  
Yu-Lu Liu
Keyword(s):  
Conserved Quantities ◽  
Elastic Rod ◽  
Thin Elastic Rod ◽  
Mei Symmetry

Cantilever Rod in Cross Wind

1989 ◽  
Vol 56 (3) ◽  
pp. 639-643 ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Numerical Integration ◽  
Large Deformation ◽  
Aerodynamic Drag ◽  
Flexural Rigidity ◽  
Relative Importance ◽  
Elastic Rod ◽  
Nondimensional Parameter ◽  
Cantilever Rod ◽  
Thin Elastic Rod

A thin elastic rod is held at one end in a strong cross wind. The nonlinear large deformation equations are formulated and solved by perturbation and numerical integration. The problem is governed by a nondimensional parameter K representing the relative importance of aerodynamic drag to flexural rigidity. For large K, phenomena such as nonuniqueness, instability, and hysteresis may occur.

scholarly journals Some exact solutions in f(𝒢,T) gravity via Noether symmetries

2017 ◽  
Vol 32 (16) ◽  
pp. 1750086 ◽  
Author(s):  
M. Farasat Shamir ◽  
Mushtaq Ahmad
Keyword(s):  
Exact Solutions ◽  
Momentum Tensor ◽  
Gravity Models ◽  
Noether Symmetry ◽  
Type I ◽  
Conserved Quantities ◽  
Rotationally Symmetric ◽  
Bianchi Type I Universe ◽  
Modified Formula ◽  
Bonnet Term

This paper is devoted to investigate the recently proposed modified Gauss–Bonnet [Formula: see text] gravity, with [Formula: see text], the Gauss–Bonnet term, coupled with [Formula: see text], the trace of energy–momentum tensor. We have used the Noether symmetry methodology to discuss some cosmologically important [Formula: see text] gravity models with anisotropic background. In particular, the Noether symmetry equations for modified [Formula: see text] gravity are reported for locally rotationally symmetric Bianchi type I universe. Explicitly, two models have been proposed to explore the exact solutions and the conserved quantities. It is concluded that the specific models of modified Gauss–Bonnet gravity may be used to reconstruct [Formula: see text]CDM cosmology without involving any cosmological constant.

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