Related papers: Analysis of constrained 2-body problem
Here the buckling of inextensible rods due to axial body forces is mapped to 1d, nonrelativistic, time-independent quantum mechanics. Focusing on the pedagogical case of rods confined to 2d, three simple and physically realizable…
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…
In order to analyze numerically inverse problems several techniques based on linear and nonlinear stability analysis are presented. These techniques are illustrated on the problem of estimating mobilities and capillary pressure in…
It is shown that a compound elastic structure, which displays a dynamic instability, may be designed as the union (or 'fusion') of two structures which are stable when separately analyzed. The compound elastic structure has two degrees of…
The attractive and repulsive linear Hookean form of gravity is known to allow for analytic solutions to N-body systems for arbitrary masses and initial conditions. This linear system is very well suited for use in the advanced undergraduate…
The exchange interaction is investigated theoretically for electrons confined to a 2-D sample placed in a linearly varying magnetic field perpendicular to the plane. Unusual and interesting behavior is predicted: starting from zero, as one…
An exact transformation method is introduced that reduces the governing equations of a continuum structure coupled to strong nonlinearities to a low dimensional equation with memory. The method is general and well suited to problems with…
This work provides a comprehensive overview of the fundamental concepts in continuum mechanics, focusing on the behaviour of materials under mechanical loads. It discusses the distinction between elastic and plastic, highlighting their…
A macroscopic theory for the dynamics of elastic, isotropic matter in presence of electromagnetic fields is proposed here. We avail of Gordon's general relativistic derivation of Abraham's electromagnetic energy tensor as starting point.…
In this work, we study pancake-shaped Bose-Einstein condensates confined by both a cylindrically symmetric harmonic potential and an optical lattice with equal periodicity in two orthogonal directions. We first identify the spectrum of the…
We classify and analyze the stability of all relative equilibria for the two-body problem in the hyperbolic space of dimension 2 and we formulate our results in terms of the intrinsic Riemannian data of the problem.
Despite being governed by the familiar laws of Hookean mechanics, elastic shells patterned with an internal structure (i.e. metashells) exhibit a wealth of unusual mechanical properties with no counterparts in unstructured materials. Here I…
In this paper we establish the existence of solutions for a model describing the evolution of a linearly viscoelastic body which is constrained to remain confined in a prescribed half-space. The confinement condition under consideration is…
An unconstrained, non-linearly elastic, semi-infinite solid is maintained in a state of large static plane strain. A power-law relation between the pre-stretches is assumed and it is shown that this assumption is well-motivated physically…
We study a new fully averaged poroelastic Kirchhoff plate model coupled with the flow of an incompressible, viscous fluid governed by the time-dependent Stokes equations. The fully averaged formulation offers several advantages over the…
A linear equation Au=f (1) with a bounded, injective, but not boundedly invertible linear operator in a Hilbert space H is studied. A new approach to solving linear ill-posed problems is proposed. The approach consists of solving a Cauchy…
We study compressible and incompressible nonlinear elasticity variational problems in a general context. Our main result gives a sufficient condition for an equilibrium to be a global energy minimizer, in terms of convexity properties of…
Various many-body models are treated, which describe $N$ points confined to move on a plane circle. Their Newtonian equations of motion ("accelerations equal forces") are integrable, i. e. they allow the explicit exhibition of $N$ constants…
A two-dimensional body, exhibiting a slight rotational movement, moves in a rarefied medium of particles which collide with it in a perfectly elastic way. In previously realized investigations by the first two authors, Plakhov & Gouveia…
Various solutions are displayed and analyzed (both analytically and numerically) of arecently-introduced many-body problem in the plane which includes both integrable and nonintegrable cases (depending on the values of the coupling…