Hojman conserved quantity deduced by weak Noether symmetry for Lagrange systems

Jia-Fang, Xie; Tie-Qiang, Gang; Feng-Xiang, Mei

doi:10.1088/1674-1056/17/2/006

Chinese Phys. B

2008

DOI: 10.1088/1674-1056/17/2/006

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Hojman conserved quantity deduced by weak Noether symmetry for Lagrange systems

Xie Jia-Fang

Gang Tie-Qiang

Mei Feng-Xiang

Abstract: Hojman conserved quantity deduced by weakNoether symmetry for Lagrange systems * Xie Jia-Fang( ) † , Gang Tie-Qiang( ), and Mei Feng-Xiang( )

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Cited by 5 publications

References 7 publications

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Conformal Invariance and a New Type of Conserved Quantities of Mechanical Systems with Variable Mass in Phase Space

Zhang¹,

Fang²,

Peng³

et al. 2009

Commun. Theor. Phys.

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Conformal invariance and a new type of conserved quantities of mechanical systems with variable mass in phase space are studied. Firstly, the definition and determining equation of conformal invariance are presented. The relationship between the conformal invariance and the Lie symmetry is given, and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry under the infinitesimal transformations is provided. Secondly, a new type of conserved quantities of the conformal invariance are obtained by using the Lie symmetry of the system. Lastly, an example is given to illustrate the application of the results.

show abstract

Conformal Invariance and a New Type of Conserved Quantities of Mechanical Systems with Variable Mass in Phase Space

Zhang¹,

Fang²,

Peng³

et al. 2009

Commun. Theor. Phys.

View full text Add to dashboard Cite

show abstract

Special Lie Symmetry and Hojman Conserved Quantity of Appell Equations for a Holonomic System

Li-Qun¹,

Jin-Chao²,

Shao-Kai³

et al. 2009

Chinese Phys. Lett.

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Special Lie symmetry and Hojman conserved quantity of Appell equations for a holonomic system are studied. Appell equations and differential equations of motion for holonomic mechanic systems are established. Under special Lie infinitesimal transformations in which the time is invariable, the determining equation of the special Lie symmetry and the expressions of Hojman conserved quantity for Appell equations of holonomic systems are presented. Finally, an example is given to illustrate the application of the results.

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Conformal invariance and conserved quantity of third-order Lagrange equations for non-conserved mechanical systems

et al. 2009

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This paper studies conformal invariance and conserved quantity of third-order Lagrange equations for nonconserved mechanical systems. Third-order Lagrange equations, the definition and a determining equation of conformal invariance of the system are presented. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The necessary and sufficient condition that conformal invariance of the system would have Lie symmetry under single-parameter infinitesimal transformations is obtained. The corresponding conserved quantity of conformal invariance is derived with the aid of a structure equation. Lastly, an example is given to illustrate the application of the results.

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Hojman conserved quantity deduced by weak Noether symmetry for Lagrange systems

Abstract: Hojman conserved quantity deduced by weakNoether symmetry for Lagrange systems * Xie Jia-Fang( ) † , Gang Tie-Qiang( ), and Mei Feng-Xiang( )

Cited by 5 publications

References 7 publications

Conformal Invariance and a New Type of Conserved Quantities of Mechanical Systems with Variable Mass in Phase Space

Conformal Invariance and a New Type of Conserved Quantities of Mechanical Systems with Variable Mass in Phase Space

Special Lie Symmetry and Hojman Conserved Quantity of Appell Equations for a Holonomic System

Conformal invariance and conserved quantity of third-order Lagrange equations for non-conserved mechanical systems

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