Related papers: Dynamical symmetries and the Ermakov invariant

We extend the second Noether theorem to optimal control problems which are invariant under symmetries depending upon k arbitrary functions of the independent variable and their derivatives up to some order m. As far as we consider a…

We present new relations derived from Noether's identity that reveal the compatibility between the components of the Hessian matrix of the Lagrangian, the infinitesimal symmetry transformation of the configuration variables and time, and a…

We discuss global tensor invariants of a rigid body motion in the cases of Euler, Lagrange and Kovalevskaya. These invariants are obtained by substituting tensor fields with cubic on variable components into the invariance equation and…

We prove a Noether type symmetry theorem to fractional problems of the calculus of variations with classical and Riemann-Liouville derivatives. As result, we obtain constants of motion (in the classical sense) that are valid along the mixed…

We study the Lie and Noether point symmetries of a class of systems of second-order differential equations with $n$ independent and $m$ dependent variables ($n\times m$ systems). We solve the symmetry conditions in a geometric way and…

The purpose of the current article is to present a brief albeit accurate presentation of the main tools used in the study of symmetries of Lagrange equations for holonomic systems and subsequently to show how these tools are applied in the…

These are intended to be review notes on emergent symmetries, i.e., symmetries which manifest themselves in specific sectors of energy in many systems. The emphasis is on the physical aspects rather than computation methods. We include some…

In this article, we present a brief overview of some of the recent progress made in identifying and generating finite dimensional integrable nonlinear dynamical systems, exhibiting interesting oscillatory and other solution properties,…

By considering the closure property of a Lagrangian multiform as a conservation law, we use Noether's theorem to show that every variational symmetry of a Lagrangian leads to a Lagrangian multiform. In doing so, we provide a systematic…

We present the Hamiltonian formalism for the Euler equation of symplectic fluids, introduce symplectic vorticity, and study related invariants. In particular, this allows one to extend D.Ebin's long-time existence result for geodesics on…

We show that a non-equilibrium diffusive dynamics in a finite-dimensional space takes in the Lagrangian frame of its mean local velocity an equilibrium form with the detailed balance property. This explains the equilibrium nature of the…

Many quantum integrable systems are obtained using an accelerator physics technique known as Ermakov (or normalized variables) transformation. This technique was used to create classical nonlinear integrable lattices for accelerators and…

Many quantum integrable systems are obtained using an accelerator physics technique known as Ermakov (or normalized variables) transformation. This technique was used to create classical nonlinear integrable lattices for accelerators and…

The last decades have seen growing interest in connecting principles of thermodynamics with methods from analytical mechanics. The thermodynamic formalism has become an inspiring framework in the study of smooth dynamical systems, and…

A hybrid framework is developed that highlights and unifies the most important aspects of the Noether correspondence between symmetries and conserved integrals in Lagrangian and Hamiltonian mechanics. Several main results are shown: (1) a…

We consider Noether symmetries within Hamiltonian setting as transformations that preserve Poincar\'e-Cartan form, i.e., as symmetries of characteristic line bundles of nondegenerate 1-forms. In the case when the Poincar\'e-Cartan form is…

For symmetric classical field theories on principal bundles there are two methods of symmetry reduction: covariant and dynamic. Assume that the classical field theory is given by a symmetric covariant Lagrangian density defined on the first…

We carry out a parallel study of the covariant phase space and the conservation laws of local symmetries in two-dimensional dilaton gravity. Our analysis is based on the fact that the Lagrangian can be brought to a form that vanishes…

We provide new insights into the contact Hamiltonian and Lagrangian formulations of dissipative mechanical systems. In particular, we state a new form of the contact dynamical equations, and we review two recently presented Lagrangian…

One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations…