Unified Symmetry of Hamilton Systems

This paper investigates the perturbation to Mei symmetry for Birkhoffian systems. The criterion equation of the perturbation to Mei symmetry is established. The condition for existence of generalized Mei adiabatic invariant induced directly from the perturbation to Mei symmetry is obtained, and its form is presented. Finally, an example is discussed to further illustrate the application of the results.

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“…If we let f = τ 0 , (12) and (13) respectively become the structure equation and the Mei exact invariant in [23].…”

Section: Criterion 1 For the Birkhoffian Systemmentioning

confidence: 99%

“…In 1927, G.D. Birkhoff made primary studies on Birkhoffian dynamics [19]. Then the researches on Birkhoffian dynamics become more and more active [20][21][22][23]. The research on perturbation to symmetries and adiabatic invariants for Birkhoffian systems has great important significance.…”

mentioning

confidence: 99%

Perturbation to Mei Symmetry and Generalized Mei Adiabatic Invariants for Birkhoffian Systems

2009

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“…Because the unified symmetry of the mechano-electrical systems is certainly a Lie symmetry, the determining equations ( 14) of the Lie symmetry hold. From expressions ( 14) and (18), using Hojman's proof method of the mechano-electrical systems, the system has the conserved quantity (19).…”

Section: Proofmentioning

confidence: 99%

Unified symmetry of mechano-electrical systems with nonholonomic constraints

et al. 2008

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The unified symmetry of mechano-electrical systems with nonholonomic constraints are studied in this paper, the definition and the criterion of unified symmetry of mechano-electrical systems with nonholonomic constraints are derived from the Lagrange–Maxwell equations. The Noether conserved quantity, Hojman conserved quantity and Mei conserved quantity are then deduced from the unified symmetry. An example is given to illustrate the application of the results.

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“…Mei symmetry, and so on. The corresponding conserved quantities are Noether conserved quantity [14][15][16], Hojman conserved quantity [17] and new type of conserved quantity [18], namely Mei conserved quantity.…”

Section: Introductionmentioning

confidence: 99%

Generalized Conformal Symmetries and Its Application of Hamilton Systems

Luo

2009

Int J Theor Phys

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In this paper the generalized conformal symmetries and conserved quantities by Lie point transformations of Hamilton systems are studied. The necessary and sufficient conditions of conformal symmetry by the action of infinitesimal Lie point transformations which are simultaneous Lie symmetry are given. This kind type determining equations of conformal symmetry of mechanical systems are studied. The Hojman conserved quantities of the Hamilton systems under infinitesimal special transformations are obtained. The relations between conformal symmetries and the Lie symmetries are derived for Hamilton systems. Finally, as application of the conformal symmetries, an illustration example is introduced.

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Unified Symmetry of Hamilton Systems

Cited by 20 publications

References 12 publications

Perturbation to Mei Symmetry and Generalized Mei Adiabatic Invariants for Birkhoffian Systems

Perturbation to Mei Symmetry and Generalized Mei Adiabatic Invariants for Birkhoffian Systems

Unified symmetry of mechano-electrical systems with nonholonomic constraints

Generalized Conformal Symmetries and Its Application of Hamilton Systems

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