On Noether symmetries and form invariance of mechanico-electrical systems
نویسندگان
چکیده
This Letter focuses on form invariance and Noether symmetries of mechanico-electrical systems. Based on the invariance of Hamiltonian actions for mechanico-electrical systems under the infinitesimal transformation of the coordinates, the electric quantities and the time, the authors present the Noether symmetry transformation, the Noether quasi-symmetry transformation, the generalized Noether quasi-symmetry transformation and the general Killing equations of Lagrange mechanico-electrical systems and Lagrange–Maxwell mechanico-electrical systems. Using the invariance of the differential equations, satisfied by physical quantities, such as Lagrangian, non-potential general forces, under the infinitesimal transformation, the authors propose the definition and criterions of the form invariance for mechanico-electrical systems. The Letter also demonstrates connection between the Noether symmetries and the form invariance of mechanico-electrical systems. An example is designed to illustrate these results. 2004 Elsevier B.V. All rights reserved.
منابع مشابه
2 Noether symmetries for two - dimensional charged particle motion
We find the Noether point symmetries for non–relativistic two-dimensional charged particle motion. These symmetries are composed of a quasi–invariance transformation, a time–dependent rotation and a time–dependent spatial translation. The associated electromagnetic field satisfy a system of first–order linear partial differential equations. This system is solved exactly, yielding three classes ...
متن کاملSystematic Derivation of Noether Point Symmetries in Special Relativistic Field Theories
A didactic and systematic derivation of Noether point symmetries and conserved currents is put forward in special relativistic field theories, without a priori assumptions about the transformation laws. Given the Lagrangian density, the invariance condition develops as a set of partial differential equations determining the symmetry transformation. The solution is provided in the case of real s...
متن کاملNoether Symmetries and Integrability in Time-dependent Hamiltonian Mechanics
We consider Noether symmetries within Hamiltonian setting as transformations that preserve Poincaré–Cartan form, i.e., as symmetries of characteristic line bundles of nondegenerate 1-forms. In the case when the Poincaré–Cartan form is contact, the explicit expression for the symmetries in the inverse Noether theorem is given. As examples, we consider natural mechanical systems, in particular th...
متن کاملNoether symmetries, energy-momentum tensors and conformal invariance in classical field theory
In the framework of classical field theory, we first review the Noether theory of symmetries, with simple rederivations of its essential results, with special emphasis given to the Noether identities for gauge theories. Will this baggage on board, we next discuss in detail, for Poincaré invariant theories in flat spacetime, the differences between the Belinfante energy-momentum tensor and a fam...
متن کاملNon-Noether symmetries and conserved quantities of nonconservative dynamical systems
This Letter focuses on studying non-Noether symmetries and conserved quantities of the nonconservative dynamical system. Based on the relationships among motion, nonconservative forces and Lagrangian, we present conservation laws on non-Noether symmetries for nonconservative dynamical systems. A criterion is obtained on which non-Noether symmetry leads to Noether symmetry in nonconservative sys...
متن کامل