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The gravitational $N$-body problem, which is fundamentally important in astrophysics to predict the motion of $N$ celestial bodies under the mutual gravity of each other, is usually solved numerically because there is no known general…
We prove that to each initial datum in a set of positive measure in phase space, there exist uncountably-many associated weak solutions of Newton's equations of motion which govern the dynamics of two non-spherical sets with real-analytic…
Neutral systems containing two identical particles, in homogeneous magnetic field are shown to obey exact factorizable solutions both in nonrelativistic and relativistic formalism, similarly to the neutral two-body systems. Concrete…
The role of gravity is crucial in astrophysics. It determines the evolution of any system, over an enormous range of time and space scales. Astronomical stellar systems as composed by N interacting bodies represent examples of…
This paper considers the energy required for collections of finite density bodies to undergo escape under internal gravitational interactions alone. As the level of the system energy is increased there are different combinations of…
The system is described by three mass-shell constraints. After a nonlinear transformation of the momenta, the analytic form taken by admissible interactions (allowing compatibility) is characterized in terms of the new variables. These…
An analytical linear solution of the fully compressible Euler equations is found, in the particular case of a stationary two dimensional flow that passes over an orographic feature with small height-width ratio. A method based on the…
We extend the equations of motion that describe non-relativistic elastic collision of two particles in one dimension to an arbitrary associative algebra. Relativistic elastic collision equations turn out to be a particular case of these…
Equations of a heavy rotating body with one fixed point can be deduced starting from a variational problem with holonomic constraints. When applying this formalism to the particular case of a Lagrange top, in the formulation with a diagonal…
We study a class of interacting, harmonically trapped boson systems at angular momentum L. The Hamiltonian leaves a L-dimensional subspace invariant, and this permits an explicit solution of several eigenstates and energies for a wide class…
We present some aspects of the rheology of field-responsive suspensions, a class of field-responsive liquid matter systems possessing the ability to undergo significant changes in their strength upon application of an external field. Both…
We analyze a mathematical model that describes the interaction between an insulating rigid body and an incompressible electrically conducting fluid surrounding it. The model as well as the mathematical analysis involve the fields of…
Following Smale, we study simple symmetric mechanical systems of $n$ point particles in the plane. In particular, we address the question of the linear and spectral stability properties of relative equilibria, which are special solutions of…
We consider the N-body problem in (1+1) dimensional lineal gravity. For 2 point masses (N=2) we obtain an exact solution for the relativistic motion. In the equal mass case we obtain an explicit expression for their proper separation as a…
We study the behaviour of a specific system of relativistic elasticity in its own gravitational field: a static, spherically symmetric shell whose wall is of arbitrary thickness consisting of hyperelastic material. We give the system of…
Newtonian dynamical systems accepting the normal shift on an arbitrary Riemannian manifold are considered. Partial differential equations forming the weak and additional normality conditions for them are reported.
We consider a problem of mass points interacting gravitationally whose motion is subjected to certain holonomic constraints. The motion of points is restricted to certain curves and surfaces. We illustrate the complicated behaviour of…
The evolution of closed gravitational systems is studied by means of $N$-body simulations. This, as well as being interesting in its own right, provides insight into the dynamical and statistical mechanical properties of gravitational…
Causal rigid particles whose action includes an {\it arbitrary} dependence on the world-line extrinsic curvature are considered. General classes of solutions are constructed, including {\it causal tachyonic} ones. The Hamiltonian…
We present a simple, analytic model for the accretion flow of an incompressible wind onto a gravitating object. This solution corresponds to the Newtonian limit of a previously known relativistic model for a fluid obeying a stiff equation…