This paper presents extensions to the traditional calculus of variations for mechanico-electrical systems containing fractional derivatives. The Euler Lagrange equations and the Hamilton formalism of the mechanico-ele...This paper presents extensions to the traditional calculus of variations for mechanico-electrical systems containing fractional derivatives. The Euler Lagrange equations and the Hamilton formalism of the mechanico-electrical systems with fractional derivatives are established. The definition and the criteria for the fractional generalized Noether quasi- symmetry are presented. Furthermore, the fractional Noether theorem and conseved quantities of the systems are obtained by virtue of the invariance of the Hamiltonian action under the infinitesimal transformations. An example is presented to illustrate the application of the results.展开更多
We investigate Noether symmetries and conservation laws of the discrete nonconserved systems with nonregular lattices.The operators of discrete transformation and discrete differentiation to the right and left are int...We investigate Noether symmetries and conservation laws of the discrete nonconserved systems with nonregular lattices.The operators of discrete transformation and discrete differentiation to the right and left are introduced for the systems.Based on the invariance of discrete Hamilton action on nonregular lattices of the systems with the nonconserved forces under the infinitesimal transformations with respect to the time and generalized coordinates,we give the discrete analog of generalized variational formula.From this formula we derive the discrete analog of generalized Noether-type identity,and then we present the generalized quasi-extremal equations and properties of these equations for the systems.We also obtain the discrete analog of Noether-type conserved laws and the discrete analog of generalized Noether theorems for the systems.We discuss an example to illustrate these results.展开更多
We investigate Noether symmetries and conservation laws of the discrete mechanico-electrical systems with nonregular lattices.The operators of discrete transformation and discrete differentiation to the right and left...We investigate Noether symmetries and conservation laws of the discrete mechanico-electrical systems with nonregular lattices.The operators of discrete transformation and discrete differentiation to the right and left are introduced for the systems.Based on the invariance of discrete Hamilton action on nonregular lattices of the systems with the dissipation forces under the infinitesimal transformations with respect to the time,generalized coordinates and generalized charge quantities,we work out the discrete analog of the generalized variational formula.From this formula we derive the discrete analog of generalized Noether-type identity,and then we present the generalized quasi-extremal equations and properties of these equations for the systems.We also obtain the discrete analog of Noether-type conserved laws and the discrete analog of generalized Noether theorems for the systems.Finally we use an example to illustrate these results.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11072218 and 60575055)
文摘This paper presents extensions to the traditional calculus of variations for mechanico-electrical systems containing fractional derivatives. The Euler Lagrange equations and the Hamilton formalism of the mechanico-electrical systems with fractional derivatives are established. The definition and the criteria for the fractional generalized Noether quasi- symmetry are presented. Furthermore, the fractional Noether theorem and conseved quantities of the systems are obtained by virtue of the invariance of the Hamiltonian action under the infinitesimal transformations. An example is presented to illustrate the application of the results.
基金supported by the National Natural Science Foundation of China(Grant Nos.10672143 and 60575055)
文摘We investigate Noether symmetries and conservation laws of the discrete nonconserved systems with nonregular lattices.The operators of discrete transformation and discrete differentiation to the right and left are introduced for the systems.Based on the invariance of discrete Hamilton action on nonregular lattices of the systems with the nonconserved forces under the infinitesimal transformations with respect to the time and generalized coordinates,we give the discrete analog of generalized variational formula.From this formula we derive the discrete analog of generalized Noether-type identity,and then we present the generalized quasi-extremal equations and properties of these equations for the systems.We also obtain the discrete analog of Noether-type conserved laws and the discrete analog of generalized Noether theorems for the systems.We discuss an example to illustrate these results.
基金supported by the National Natural Science Foundation of China(Grant Nos 10672143 and 60575055)
文摘We investigate Noether symmetries and conservation laws of the discrete mechanico-electrical systems with nonregular lattices.The operators of discrete transformation and discrete differentiation to the right and left are introduced for the systems.Based on the invariance of discrete Hamilton action on nonregular lattices of the systems with the dissipation forces under the infinitesimal transformations with respect to the time,generalized coordinates and generalized charge quantities,we work out the discrete analog of the generalized variational formula.From this formula we derive the discrete analog of generalized Noether-type identity,and then we present the generalized quasi-extremal equations and properties of these equations for the systems.We also obtain the discrete analog of Noether-type conserved laws and the discrete analog of generalized Noether theorems for the systems.Finally we use an example to illustrate these results.
