Carlo Ferrario

Symmetries and constants of motion for constrained Lagrangian systems: a presymplectic version of the Noether theorem

The concept of dynamical symmetry for constrained Lagrangian systems is analysed and generalized. Both the direct and converse Noether theorems are proved for singular Lagrangians.

Generalization of the Lorenz model to the two-dimensional convection of second-grade fluids

Abstract We apply the truncation of the Navier–Stokes–Fourier equations which leads to the Lorenz model, to the investigation of second-grade fluids. The new set of equations proves to work as an approximated approach to 2D-convective dynamics, under the same restrictions as for Newtonian fluids. The different behaviour depends only on α 1 and consists in a “modified” Prandtl number.

Theoretical Results on Steady Convective Flows between Horizontal Coaxial Cylinders

For arbitrary Rayleigh number,

Symmetries in Lagrangian dynamics

\mathrm{Ra}

Dynamical symmetries in constrained systems: a Lagrangian analysis

, Prandtl number, and any ratio of the cylindrical radii, existence of steady solutions of the two-dimensional Oberbeck–Boussinesq system is proved in Theorem 3.5. We show nonlinear stability for large values of the aspect ratio and

Lagrangian constraints and gauge symmetries

\mathrm{Ra}<\mathrm{Ra}_L

Comment on `Exploring a rheonomic system'

, for some number

Transformation properties of the Lagrange function

\mathrm{Ra}_L

Dirac quantization of a particle subject to apparent forces

which is bounded from below (cf. Theorem 4.4). We prove that for large aspect ratio,

Infinitesimal transformations and equivalence of the Lagrangian and Hamiltonian descriptions

\mathrm{Ra}_L