Related papers: The second Noether theorem on time scale

We prove a fractional Noether's theorem for fractional Lagrangian systems invariant under a symmetry group both in the continuous and discrete cases. This provides an explicit conservation law (first integral) given by a closed formula…

In this note I provide two extensions of a particular case of the classical Poncelet theorem.

Noether's 2nd theorem applied to a total system states that a global symmetry which is a part of local symmetries does not provide a physically meaningful conserved charge but it instead leads to off-shell constraints as a form of conserved…

We prove a DuBois-Reymond necessary optimality condition and a Noether symmetry theorem to the recent quantum variational calculus of Cresson. The results are valid for problems of the calculus of variations with functionals defined on sets…

We prove a necessary optimality condition of Euler-Lagrange type for variational problems on time scales involving nabla derivatives of higher-order. The proof is done using a new and more general fundamental lemma of the calculus of…

We prove two general theorems which determine the Lie and the Noether point symmetries for the equations of motion of a dynamical system which moves in a general Riemannian space under the action of a time dependent potential…

We summarize the use of Noether symmetries in Minisuperspace Quantum Cosmology. In particular, we consider minisuperspace models, showing that the existence of conserved quantities gives selection rules that allow to recover classical…

English version of abstract: The dynamic optimization problems treated by the calculus of variations are usually solved with the help of the 2nd order Euler-Lagrange differential equations. These equations are, generally speaking,…

We review the recent generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives and study them using indirect methods. In particular, we provide necessary…

In a series of previous articles by the author, it was shown that one could effectively give a variational formulation to non-conservative mechanical systems, as well as ones that subject to non-holonomic constraints by starting with the…

We summarize here the first results obtained using a technique we recently developed for the Noether analysis of Hopf-algebra spacetime symmetries, including the derivation of conserved charges for field theories in noncommutative…

The $n$-time generalization of Schwarzschild solution is considered. The equations of geodesics for the metric are integrated. The multitemporal analogues of Newton laws for the extended objects described by the solution are suggested. The…

The calculus of variations is a classical subject which has gain throughout the last three hundred years a level of rigor and elegance that only time can give. In this note we show that, contrary to the classical field, available…

When discussing consequences of symmetries of dynamical systems based on Noether's first theorem, most standard textbooks on classical or quantum mechanics present a conclusion stating that a global continuous Lie symmetry implies the…

Local Schauder estimates hold in the nonuniformly elliptic setting. Specifically, first derivatives of solutions to nonuniformly elliptic variational problems and elliptic equations are locally H\"older continuous, provided coefficients are…

We give a proper fractional extension of the classical calculus of variations. Necessary optimality conditions of Euler-Lagrange type for variational problems containing both classical and fractional derivatives are proved. The fundamental…

We consider the second variational derivative of a given gauge-natural invariant Lagrangian taken with respect to (prolongations of) vertical parts of gauge-natural lifts of infinitesimal principal automorphisms. By requiring such a second…

We establish a new version of the first Noether Theorem, according to which the (equivalence classes of) first integrals of given Euler-Lagrange equations in one independent variable are in exact one-to-one correspondence with the…

Noether's calculus of invariant variations yields exact identities from functional symmetries. The standard application to an action integral allows to identify conservation laws. Here we rather consider generating functionals, such as the…

In this paper, within the framework of the consistent approach recently introduced for approximate Lie symmetries of differential equations, we consider approximate Noether symmetries of variational problems involving small terms. Then, we…