scholarly journals Conformal invariance, Noether symmetry and Lie symmetry for systems with unilateral Chetaev non-holonomic constraints

2012 ◽  
Vol 61 (14) ◽  
pp. 141101
Author(s):  
Chen Rong ◽  
Xu Xue-Jun
Keyword(s):  
Conformal Invariance ◽  
Lie Symmetry ◽  
Noether Symmetry ◽  
Holonomic Constraints

scholarly journals Symmetry Preserving Discretization of the Hamiltonian Systems with Holonomic Constraints

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2959
Author(s):  
Lili Xia ◽  
Mengmeng Wu ◽  
Xinsheng Ge
Keyword(s):  
Difference Scheme ◽  
Exact Solutions ◽  
Hamiltonian Systems ◽  
Lie Symmetry ◽  
Numerical Schemes ◽  
Holonomic Constraints ◽  
Holonomic Systems ◽  
Difference Type ◽  
The Difference ◽  
Discrete Invariants

Symmetry preserving difference schemes approximating equations of Hamiltonian systems are presented in this paper. For holonomic systems in the Hamiltonian framework, the symmetrical operators are obtained by solving the determining equations of Lie symmetry with the Maple procedure. The difference type of symmetry preserving invariants are constructed based on the three points of the lattice and the characteristic equations. The difference scheme is constructed by using these discrete invariants. An example is presented to illustrate the applications of the results. The solutions of the invariant numerical schemes are compared to the noninvariant ones, the standard and the exact solutions.

Lie and Noether symmetry analysis in Brans–Dicke cosmology

2018 ◽  
Vol 33 (34) ◽  
pp. 1850198 ◽  
Author(s):  
Sourav Dutta ◽  
Santu Mondal
Keyword(s):  
Evolution Equations ◽  
Analytic Solution ◽  
State Parameter ◽  
Lie Symmetry ◽  
Noether Symmetry ◽  
Coordinate Systems ◽  
Group Invariant ◽  
Augmented System ◽  
Equation Of State Parameter ◽  
Group Invariant Solutions

This paper is aimed to study the group invariant solutions of the evolution equations in Brans–Dicke cosmology. In this context, we have considered the flat homogeneous Brans–Dicke (BD) scalar field in the background of flat homogeneous and isotropic Friedmann–Lemaître–Robertson–Walker (FLRW) cosmological model and have used Lie and Noether symmetry on the augmented system. From Lie symmetry we have determined the unknown potential for two different values of the equation of state parameter w. Then assuming that the Lagrangian admits a Noether symmetry, an analytic solution of the system is obtained in both old and new coordinate systems.

scholarly journals Mei symmetry, Noether symmetry and Lie symmetry of an Emden system

2006 ◽  
Vol 55 (11) ◽  
pp. 5594
Author(s):  
Gu Shu-Long ◽  
Zhang Hong-Bin
Keyword(s):  
Lie Symmetry ◽  
Noether Symmetry ◽  
Mei Symmetry
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