On the Relationship between Two Notions of Compatibility for Bi-Hamiltonian Systems

Bi-Hamiltonian structures are of great importance in the theory of integrable Hamiltonian systems. The notion of compatibility of symplectic structures is a key aspect of bi-Hamiltonian systems. Because of this, a few different notions of compatibility have been introduced. In this paper we show that, under some additional assumptions, compatibility in the sense of Magri implies a notion of compatibility due to Fass`o and Ratiu, that we dub bi-affine compatibility. We present two proofs of this fact. The first one uses the uniqueness of the connection parallelizing all the Hamiltonian vector fields tangent to the leaves of a Lagrangian foliation. The second proof uses Darboux–Nijenhuis coordinates and symplectic connections

Gravitational and Harmonic Oscillator Potentials on Surfaces of Revolution

In this paper, we consider the motion of a particle on a surface of revolution under the influence of a central force field. We prove that there are at most two analytic central potentials for which all the bounded, nonsingular orbits are closed and that there are exactly two on some surfaces with constant Gaussian curvature. The two potentials leading to closed orbits are suitable generalizations of the gravitational and harmonic oscillator potential. We also show that there could be surfaces admitting only one potential that leads to closed orbits. In this case, the potential is a generalized harmonic oscillator. In the special case of surfaces of revolution with constant Gaussian curvature, we prove a generalization of the well-known Bertrand theorem

Design and optimization of fuel injection of a 50 kW micro turbogas

The present article deals with the design of a micro turbogas turbine suitable for on board applications, e.g., as a power generator on hybrid transit bus, characterized by a simple constructive approach. Deriving the machine layout from an existing KJ-66 aircraft model engine, the authors propose a theoretical design of a compact, lightweight turbogas turbine, by investigating the technical possibility and limits of the proposed design. In particular, a different combustion chamber layout has been proposed, and fuel adduction channels for different swirler designs have been simulated via ANSYS Fluent in order to identify a satisfactory fuel spreading. As a result, the complete characterization of the design parameters and geometries has been performed, and a series of RANS simulations has been used in order to identify an optimal swirler configuration