C. Galeş

On the Dynamics of Space Debris: 1:1 and 2:1 Resonances

We study the dynamics of the space debris in the 1:1 and 2:1 resonances, where geosynchronous and GPS satellites are located. By using Hamiltonian formalism, we consider a model including the geopotential contribution for which we compute the secular and resonant expansions of the Hamiltonian. Within such model we are able to detect the equilibria and to study the main features of the resonances in a very effective way. In particular, we analyze the regular and chaotic behavior of the 1:1 and 2:1 resonant regions by analytical methods and by computing the Fast Lyapunov Indicators, which provide a cartography of the resonances. This approach allows us to detect easily the location of the equilibria, the amplitudes of the libration islands and the main dynamical stability features of the resonances, thus providing an overview of the 1:1 and 2:1 resonant domains under the effect of Earth’s oblateness. The results are validated by a comparison with a model developed in Cartesian coordinates, including the geopotential, the gravitational attraction of Sun and Moon and the solar radiation pressure.

Some uniqueness and continuous dependence results in the theory of swelling porous elastic soils

This paper is concerned with the isothermal linear theory of swelling porous elastic soils. Initial-boundary value problems are formulated for the linear dynamic theory of an isothermal mixture consisting of three components: an elastic solid, a viscous fluid and a gas. Then the uniqueness and continuous dependence problems are discussed in connection with the solutions of such initial-boundary value problems. The uniqueness results are established under mild positive semi-definiteness assumptions or with no definiteness assumptions upon the internal energy. Various estimates are established for describing the continuous dependence of solutions with respect to the external given data. In this aim the Lagrange identity and the logarithmic convexity methods are used.

A Mixture Theory for Microstretch Thermoviscoelastic Solids

A nonlinear theory is developed for a heat-conducting viscoelastic composite which is modelled as a mixture consisting of a microstretch Kelvin–Voigt material and a microstretch elastic solid. The strain measures, the basic laws and the constitutive equations are established and presented in Lagrangian description. The initial boundary value problem associated to such model is also formulated. Then the linearized theory is considered and the constitutive equations are given for both anisotropic and isotropic bodies. Finally, a uniqueness result is established within the framework of the linear theory.

On Spatial Behavior of the Harmonic Vibrations in Thermoviscoelastic Mixtures

This paper concerns the study of time–harmonic vibrations for homogeneous and anisotropic thermoviscoelastic mixtures. The dissipative effects are used to introduce an appropriate measure associated with the amplitude of the steady–state vibrations and to establish an exponential decay estimate of Saint–Venant type, which holds for every value of the frequency of vibrations and for arbitrary values of the elastic coefficients.

On the spatial behavior in the theory of swelling porous elastic soils

Abstract This paper is concerned with the study of the spatial behavior of the processes associated with a mixture consisting of three components: an elastic solid, a viscous fluid and a gas. An appropriate time-weighted surface power function is used in order to describe the spatial behavior of the processes in question. Spatial estimates of Saint–Venant type (for bounded bodies) and Phragmen–Lindelof type (for unbounded bodies) with time-dependent and time-independent rates are established. For unbounded bodies the asymptotic spatial behavior of the processes is also studied by means of an appropriate volumetric measure.

Some Results in the Dynamics of Viscoelastic Mixtures

The present article studies some qualitative properties of solutions in the dynamics of viscoelastic mixtures made by two constituents: a porous elastic solid and a viscous fluid. In this sense, some results concerning the theory of semigroups of linear operators are used to establish the existence and uniqueness of the weak solutions of the initial boundary value problems associated with the linear theory. The continuous dependence problem upon initial data and supply terms is also investigated. Then, the temporal behavior is studied in terms of the Cesáro means of various parts of the total energy. The relations that describe the asymptotic behavior of mean energies are established by using some Lagrange—Brun identities.

A mixture theory for micropolar thermoelastic solids.

We derive a nonlinear theory of heat-conducting micropolar mixtures in Lagrangian description. The kinematics, balance laws, and constitutive equations are examined and utilized to develop a nonlinear theory for binary mixtures of micropolar thermoelastic solids. The initial boundary value problem is formulated. Then, the theory is linearized and a uniqueness result is established.

Asymptotic Partition of Energy in Micromorphic Thermopiezoelectricity

The Cesàro means of various parts of the total energy are introduced in the context of the linear theory of micromorphic thermopiezoelectricity. Then, using some Lagrange identities, the relations describing the asymptotic behavior of the Cesàro means are established.

A Study of the Lunisolar Secular Resonance 2ω˙+Ω˙=0

The dynamics of small bodies around the Earth has gained a renewed interest, since the awareness of the problems that space debris can cause in the nearby future. A relevant role in space debris is played by lunisolar secular resonances, which might contribute to an increase of the orbital elements, typically of the eccentricity. We concentrate our attention on the lunisolar secular resonance described by the relation

On spatial behavior in linear viscoelasticity

2\dot{\omega}+\dot{\Omega}=0