Conformal invariance and conserved quantities for a higher-order Lagrange system by Lie point transformation of groups are studied.The differential equation of motion for the higher-order Lagrange system is introduced...Conformal invariance and conserved quantities for a higher-order Lagrange system by Lie point transformation of groups are studied.The differential equation of motion for the higher-order Lagrange system is introduced.The definition of conformal invariance for the system together with its determining equations and conformal factor are provided.The necessary and sufficient condition that the system’s conformal invariance would be Lie symmetry by the infinitesimal one-parameter point transformation group is deduced.The conserved quantity of the system is derived using the structural equation satisfied by the gauge function.An example of a higher-order mechanical system is offered to illustrate the application of the result.展开更多
Based on not only the ideas of phenomenological investigations about the internal friction of crystalline materials but also the studies on the internal friction laws of noncrystalline materials during structural rela...Based on not only the ideas of phenomenological investigations about the internal friction of crystalline materials but also the studies on the internal friction laws of noncrystalline materials during structural relaxation processes in recent years,the method of making relaxation cell is put out.In the method,traditional mechanics parameter model and two-level model are unified,so phenomenological studies on the internal friction of noncrystalline materials during structural relaxation processes are made and a new relaxation law is formed.展开更多
基金by the National Natural Science Foundation of China under Grant No 10772025.
文摘Conformal invariance and conserved quantities for a higher-order Lagrange system by Lie point transformation of groups are studied.The differential equation of motion for the higher-order Lagrange system is introduced.The definition of conformal invariance for the system together with its determining equations and conformal factor are provided.The necessary and sufficient condition that the system’s conformal invariance would be Lie symmetry by the infinitesimal one-parameter point transformation group is deduced.The conserved quantity of the system is derived using the structural equation satisfied by the gauge function.An example of a higher-order mechanical system is offered to illustrate the application of the result.
文摘Based on not only the ideas of phenomenological investigations about the internal friction of crystalline materials but also the studies on the internal friction laws of noncrystalline materials during structural relaxation processes in recent years,the method of making relaxation cell is put out.In the method,traditional mechanics parameter model and two-level model are unified,so phenomenological studies on the internal friction of noncrystalline materials during structural relaxation processes are made and a new relaxation law is formed.
