G. Platania

Inverse problem in classical mechanics: dissipative systems

We show how the ambiguity of Lagrangian and Hamiltonian descriptions for conservative systems gives rise to an analogous ambiguity for dissipative systems. For a subclass of them we also give a Lagrangian description.

Scalar fields and matter cosmologies

Abstract We have extended the FRW scalar field cosmology including matter. We have discussed exact solutions for potentials like V(ϕ)=0 and (only in presence of dust) V(ϕ)=αeηϕ+e-ηϕ.

New exact solutions of cosmological equations with considerations upon the cosmological constant

Abstract The cosmological equations of a gravitational field, minimally coupled witha scalar field, are exactly integrated, provided that the potential of the scalar field belongs to a special class of exponentials. A particular solution is given, exhibiting the damping of the effective cosmological constant and a power-law inflation.

Inflationary models in ECSK theory

Abstract We have extended the Guth inflationary model of the universe to the Einstein-Cartan theory of gravitation. In this model the initial singularity is avoided; moreover, the minimal radius of the universe is influenced by the fals vacuum energy.

The dynamical behavior of scalar fields near the initial singularity

Analyzing the Klein-Gordon equation in a homogeneous, Isotropic and spatially flat universe model, we find the conditions for the existence of a universe dominated by a scalar field in its early stages.

Properties of a spin fluid in a Riemann-Cartan spacetime

Abstract In this paper we extend to the case of spin fluids in the Einstein-Cartan theory some results obtained by Taub and Lichnerowicz for a perfect fluid in general relativity. So doing we also give an extension of the Bernoulli theorem. We show a connection between torsion and a macroscopical quantity, the tensor Ω ij =2∇[ j V i ] .

Homogeneous isotropic Newtonian cosmology and the Clebsch generalized potentials

SummaryWe construct the kinetic potentials that appear on the generalized Clebsch representation for the velocity field of a perfect fluid with a politropic state equation that describes the matter distribution in a Newtonian homogeneous isotropic universe. We also specify the constants of motion with respect to the HS group.RiassuntoSi costituiscono i potenziali cinetici che appaiono nella rappresentazione generalizzata di Clebsch per il campo di velocità di un fluido perfetto descrivente la distribuzione di materia nel caso di un universo newtoniano omogeneo ed isotropo. Sempre in questo caso si specificano, inoltre, le costanti del moto relative al gruppo di Heckmann-Shucking.РезюмеМы конструируем кинетические потенциалы, которые появляются в обобщенном представлении Клебша для поля скоростей идеальной жидкости с политропным уравнением состояния, которое описывает распределение вещества в ньютоновой однородной изотропной вселенной. Мы определяем постоянные движения относительно HS группы.