Computing globally efficient solutions is a major challenge in optimal control of nonlinear dynamical systems. This work proposes a method combining local optimization and motion planning techniques based on exploiting inherent dynamical systems structures, such as symmetries and invariant manifolds. Prior to the optimal control, the dynamical system is analyzed for structural properties that c...

By considering the nonrelativistic limit of de-Sitter geometry one obtains the nonrelativistic space-time with a cosmological constant and Newton-Hooke (NH) symmetries. We show that the NH symmetry algebra can be enlarged by the addition of the constant acceleration generators and endowed with central extensions (one in any dimension (D) and three in D=(2+1)). We present a classical Lagrangian ...

In [Gi3] Givental introduced and studied a space of formal genus zero Gromov-Witten theories GW0, i.e. functions satisfying string and dilaton equations and topological recursion relations. A central role in the theory plays the geometry of certain Lagrangian cones and a twisted symplectic group of hidden symmetries. In this note we show that the Lagrangian cones description of the action of th...

In the Lagrangian framework for symmetries and conservation laws of field theories, we investigate globality properties of conserved currents associated with non–global Lagrangians admitting global Euler–Lagrange morphisms. Our approach is based on the recent geometric formulation of the calculus of variations on finite order jets of fibered manifolds in terms of variational sequences.

We add to Galilean symmetries the transformations describing constant accelerations. The corresponding extended Galilean algebra allows, in any dimension D = d + 1, the introduction of one central charge c while in D = 2 + 1 we can have three such charges: c, θ and θ. We present nonrelativistic classical mechanics models, with higher order time derivatives and show that they give dynamical real...

Noether-like operators play an essential role in writing down the first integrals for Euler-Lagrange systems of ordinary differential equations (ODEs). The classification of such operators is carried out with the help of analytic continuation of Lagrangians on the line. We obtain the classification of 5, 6 and 9 Noether-like operators for two-dimensional Lagrangian systems that arise from the s...

The transition operator for the radiative capture of mesons μ− by protons is constructed starting from a chiral Lagrangian of the Nπρa1 ω system obtained within the approach of hidden local symmetries. The transition operator is gauge invariant and satisfies exactly the CVC and PCAC equations.

Gauge invariance is a powerful tool to determine the dynamics of the electroweak and strong forces. The particle content, structure and symmetries of the Standard Model Lagrangian are discussed. Special emphasis is given to the many phenomenological tests which have established this theoretical framework as the Standard Theory of electroweak interactions.

New symmetry transformations for the n-dimensional Toda lattice are presented. Their existence allows for the construction of several first order Lagrangian structures associated to them. The multi-Hamiltonian structures are derived from Lagrangians in detail. The set of symmetries generates a Lie algebra.

An effective lagrangian incorporating both chiral and heavy quark symmetries and describing the low momentum interactions of heavy mesons and light scalar and vector resonances is presented. Using some available data and assuming nearest pole dominance for the form factors we can calculate, at the leading order in chiral and heavy quark expansion, semileptonic B and D decays into light mesons.