Mei symmetry and new conserved quantities for non-material volumes

Jiang, Wen-An; Liu, K.; Xia, Zhaowang; Chen, M.

doi:10.1007/s00707-018-2200-9

Cited by 10 publications

(7 citation statements)

References 19 publications

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“…Mei symmetries of the rotational relativistic mass variable system are discussed in [5], with a focus on the relationship between Lie and Mei symmetries. Jiang et al [6] constructed the Mei symmetries for non-material volumes. A single-degree-offreedom non-material volume is taken as an example to determine the conserved quantities.…”

Section: Introductionmentioning

confidence: 99%

First-Order Approximate Mei Symmetries and Invariants of the Lagrangian

Kausar

Ферозе

2022

Mathematics

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In this article, the formulation of first-order approximate Mei symmetries and Mei invariants of the corresponding Lagrangian is presented. Theorems and determining equations are given to evaluate approximate Mei symmetries, as well as approximate first integrals corresponding to each symmetry of the associated Lagrangian. The formulated procedure is explained with the help of the linear equation of motion of a damped harmonic oscillator (DHO). The Mei symmetries corresponding to the Lagrangian and Hamiltonian of DHO are compared.

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Section: Introductionmentioning

confidence: 99%

First-Order Approximate Mei Symmetries and Invariants of the Lagrangian

Kausar

Ферозе

2022

Mathematics

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“…F Jian-Hui [12] discussed the Mei symmetries of the rotational relativistic mass variable system, with a focus on the link between Lie and Mei symmetries. The Mei symmetries for non-material volumes were discovered by Jiang et al [13]. To determine the conserved quantities, a singledegree-of-freedom non-material volume is used as an example.…”

Section: Introductionmentioning

confidence: 99%

The Mei Symmetries for the Lagrangian Corresponding to the Schwarzschild Metric and the Kerr Black Hole Metric

2022

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In this paper, the Mei symmetries for the Lagrangians corresponding to the spherically and axially symmetric metrics are investigated. For this purpose, the Schwarzschild and Kerr black hole metrics are considered. Using the Mei symmetries criterion, we obtained four Mei symmetries for the Lagrangian of Schwarzschild and Kerr black hole metrics. The results reveal that, in the case of the Schwarzschild metric, the obtained Mei symmetries are a subset of the Lie point symmetries of equations of motion (geodesic equations), while in the case of the Kerr black hole metric, the Noether symmetry set is a subset of the Mei symmetry set and that Mei symmetries and the Lie point symmetries of the equations of motion are same.

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“…Correspondingly, the Hojman conservation laws can be derived [5,8,9]. The Mei symmetry we are going to study was first proposed by Professor Mei in 2000 [10] and later popularized by many scholars [11][12][13][14][15][16][17]. Compared with Noether or Lie symmetry, Mei symmetry is a new kind of symmetry, and it refers to the invariance that the dynamic functions after infinitesimal transformation still make the dynamic equations hold.…”

Section: Introductionmentioning

confidence: 99%

Mei Symmetry and Conservation Laws for Time-Scale Nonshifted Hamilton Equations

Zhang

2021

Advances in Mathematical Physics

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The Mei symmetry and conservation laws for time-scale nonshifted Hamilton equations are explored, and the Mei symmetry theorem is presented and proved. Firstly, the time-scale Hamilton principle is established and extended to the nonconservative case. Based on the Hamilton principles, the dynamic equations of time-scale nonshifted constrained mechanical systems are derived. Secondly, for the time-scale nonshifted Hamilton equations, the definitions of Mei symmetry and their criterion equations are given. Thirdly, Mei symmetry theorems are proved, and the Mei-type conservation laws in time-scale phase space are driven. Two examples show the validity of the results.

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Mei symmetry and new conserved quantities for non-material volumes

Cited by 10 publications

References 19 publications

First-Order Approximate Mei Symmetries and Invariants of the Lagrangian

First-Order Approximate Mei Symmetries and Invariants of the Lagrangian

The Mei Symmetries for the Lagrangian Corresponding to the Schwarzschild Metric and the Kerr Black Hole Metric

Mei Symmetry and Conservation Laws for Time-Scale Nonshifted Hamilton Equations

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