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Perturbation to Mei symmetry and Mei adiabatic invariants for mechanical systems in phase space 下载免费PDF全文
For a perturbed mechanical system in phase space, considering d/dt in the structure equation and process of proof including infinitesimal parameter ε obviously, this paper studies the perturbation to Mei symmetry and adiabatic invariants. Firstly, the exact invariant induced directly from the Mei symmetry of the system without perturbation is given. Secondly, based on the concept of high-order adiabatic invariant, the determining equations of the perturbation to Mei symmetry are established, the condition of existence of the Mei adiabatic invariant led by the perturbation to Mei symmetry is obtained, and its form is presented. Lastly, an example is given to illustrate the application of the results. 相似文献
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A New type of conserved quantity deduced from Mei symmetry of nonholonomic systems in terms of quasi-coordinates 下载免费PDF全文
This paper studies the new type of conserved quantity which is directly induced by Mei symmetry of nonholonomic systems in terms of quasi-coordinates. A coordination function is introduced, and the conditions for the existence of the new conserved quantities as well as their forms are proposed. Some special cases are given to illustrate the generalized significance of the new type conserved quantity. Finally, an illustrated example is given to show the
application of the nonholonomic system's results. 相似文献
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Conformal invariance and conserved quantity of third-order Lagrange equations for non-conserved mechanical systems 下载免费PDF全文
This paper studies conformal invariance and conserved
quantity of third-order Lagrange equations for non-conserved
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. 相似文献
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Perturbation to Mei Symmetry and Generalized Mei Adiabatic Invariants for Nonholonomic Systems in Terms of Quasi-Coordinates 下载免费PDF全文
By introducing the coordination function f, the generalized Mei conserved quantities for the nonholonomic systems in terms of quasi-coordinates are given. Then based on the concept of adiabatic invariant, the perturbation to Mei symmetry and the generalized Mei adiabatic invariants for nonholonomic systems in terms of quasi-coordinates are studied. 相似文献
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A new type of conserved quantity which is directly induced by the Mei symmetry of the holonomic system is studied. Firstly, the definition and criterion of the Mei symmetry for a holonomic mechanical system is given. Secondly, the condition of existence of the new conserved quantity as well as its form is obtained. Lastly, an example is given to illustrate the application of the results. 相似文献
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Perturbation to Noether Symmetry and Noether Adiabatic Invariants of General Discrete Holonomic Systems 下载免费PDF全文
The perturbation to Noether symmetry and Noether adiabatic invariants of general discrete holonomic systems are studied. First, the discrete Noether exact invariant induced directly from the Noether symmetry of the system without perturbation is given. Secondly, the concept of discrete high-order adiabatic invariant is presented, the criterion of the perturbation to Noether symmetry is established, and the discrete Noether adiabatic invariant induced directly from the perturbation to Noether symmetry is obtained. Lastly, an example is discussed to illustrate the application of the results. 相似文献
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