Conformal invariance of Mei symmetry for the non-holonomic systems of non-Chetaev’s type

Jian-Le, Cai

doi:10.1007/s11071-011-0279-9

Cited by 32 publications

(9 citation statements)

References 30 publications

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“…The key question to the conformal invariance of dynamics is to find out the conformal factor. Considerable progress has made over past years in the application of conformal invariance to mechanical systems [21][22][23][24][25][26]. However, the application of conformal invariance to thin elastic rod has never been investigated.…”

Section: Introductionmentioning

confidence: 99%

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

Wang

Feng

2017

Acta Phys. Pol. A

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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.

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Section: Introductionmentioning

confidence: 99%

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

Wang

Feng

2017

Acta Phys. Pol. A

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“…The key question to the conformal invariance of dynamics is to find out the conformal factor. Considerable progress has been made over past years in the application of conformal invariance to mechanical systems [20][21][22][23][24][25]45]. However, the application of conformal invariance to thin elastic rod has never been investigated.…”

Section: Introductionmentioning

confidence: 99%

Conformal invariance of Mei symmetry and conserved quantities of Lagrange equation of thin elastic rod

Wang

Xue

2015

Nonlinear Dyn

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By Kirchhoff dynamic analogy, the thin elastic rod static equals to rotation of rigid body dynamic. The analytical mechanics methods reflect their advantages in the study of the modeling and equilibrium and stability of elastic rod static, especially for the constrained problems. The Lagrangian structure of the equation of motion for elastic rod is deduced from the integral variational principle. The definition of conformal invariance of Mei symmetry of elastic rod in Lagrangian form is given. The determining equation of conformal invariance of Mei symmetry is obtained based on the Lie point transformation group. The relation between conformal invariance of Mei symmetry and Mei symmetry is discussed. The structure equation and conserved quantity by using the Lagrangian structure along arc coordinate deduced from conformal invariance of Mei symmetry of elastic rod are constructed. Take rod with circular cross section as example to illustrate the application of the results get in this paper. These conserved quantities will be helpful in the study of exact solutions and stability, as well as the numerical simulation of the thin elastic rod nonlinear mechanics.

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“…In recent years, the studies on the dynamics for nonholonomic systems have made great progress [1][2][3][4][5][6][7][8]. In addition, the studies about Noether symmetry and Noether conserved quantity [9][10][11][12], Lie symmetry and Hojman conserved quantity [13][14][15][16][17][18][19][20][21], Mei symmetry and Mei conserved quantity [22][23][24][25][26][27][28][29][30][31][32] for mechanical systems have gained many achievements. A special nonholonomic system whose constraint equations contain a small parameter is called a weakly nonholonomic system.…”

Section: Introductionmentioning

confidence: 99%

Lie Symmetry and Approximate Hojman Conserved Quantity of Lagrange Equations for a Weakly Nonholonomic System

et al. 2013

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The Lie symmetry and Hojman conserved quantity of Lagrange equations for a weakly nonholonomic system and its first-degree approximate holonomic system are studied. The differential equations of motion for the system are established. Under the special infinitesimal transformations of group in which the time is invariable, the definition of the Lie symmetry for the weakly nonholonomic system and its first-degree approximate holonomic system are given, and the exact and approximate Hojman conserved quantities deduced directly from the Lie symmetry are obtained. Finally, an example is given to study the exact and approximate Hojman conserved quantity for the system.

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Conformal invariance of Mei symmetry for the non-holonomic systems of non-Chetaev’s type

Cited by 32 publications

References 30 publications

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

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

Conformal invariance of Mei symmetry and conserved quantities of Lagrange equation of thin elastic rod

Lie Symmetry and Approximate Hojman Conserved Quantity of Lagrange Equations for a Weakly Nonholonomic System

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