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Conformal invariance and Noether symmetry, Lie symmetry of holonomic mechanical systems in event space
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This paper is devoted to studying the conformal invariance
and Noether symmetry and Lie symmetry of a holonomic mechanical
system in event space. The definition of the conformal invariance
and the corresponding conformal factors of the holonomic system in
event space are given. By investigating the relation between the
conformal invariance and the Noether symmetry and the Lie symmetry,
expressions of conformal factors of the system under these
circumstances are obtained, and the Noether conserved quantity and
the Hojman conserved quantity directly derived from the conformal
invariance are given. Two examples are given to illustrate the
application of the results. 相似文献
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This paper studies the conformal invariance and conserved quantities
of general holonomic systems in phase space. The definition and the
determining equation of conformal invariance for general holonomic
systems in phase space are provided. The conformal factor expression
is deduced from conformal invariance and Lie symmetry. The
relationship between the conformal invariance and the Lie symmetry
is discussed, and the necessary and sufficient condition that the
conformal invariance would be the Lie symmetry of the system under
the infinitesimal single-parameter transformation group is deduced.
The conserved quantities of the system are given. An example is
given to illustrate the application of the result. 相似文献
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Conformal Invariance and Conserved Quantities of General Holonomic Systems 总被引:1,自引:0,他引:1
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Conformed invariance and conserved quantities of general holonomic systems are studied. A one-parameter infinitesimal transformation group and its infinitesimal transformation vector of generators are described. The definition of conformal invariance and determining equation for the system are provided. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The necessary and suttlcient condition, that conformal invariance of the system would be Lie symmetry, is obtained under the infinitesimal one-parameter transformation group. The corresponding conserved quantity is derived with the aid of a structure equation. Lastly, an example is given to demonstrate the application of the result. 相似文献