Related papers: Elastica as a dynamical system
The formalism of the particle dynamics in the space-time, where motion of free particles is primordially stochastic, is considered. The conventional dynamic formalism, obtained for the space-time, where the motion of free particles is…
We revisit the classical problem of the planar Euler \emph{elastica} with applied forces and moments, and present a classification of the shapes in terms of tangentially conserved quantities associated with spatial and material symmetries.…
Quasi-static strain-controlled measurements of stress vs strain curves in macroscopic amorphous solids result in a nonlinear looking curve that ends up either in mechanical collapse or in a steady-state with fluctuations around a mean…
Acousto-elasticity is concerned with the propagation of small-amplitude waves in deformed solids. Results previously established for the incremental elastodynamics of exact non-linear elasticity are useful for the determination of third-…
We construct time independent configurations of two gravitating elastic bodies. These configurations either correspond to the two bodies moving in a circular orbit around their center of mass or strictly static configurations.
What is the demand elasticity of statistical arbitrageurs that invest according to the advice of modern cross-sectional asset pricing models? Thirteen models from the literature exhibit strikingly inelastic demand, in contrast to classical…
Capillary forces acting at the surface of a liquid drop can be strong enough to deform small objects and recent studies have provided several examples of elastic instabilities induced by surface tension. We present such an example where a…
Almost all available results in elasticity on curved topographies are obtained within either a small curvature expansion or an empirical covariant generalization that accounts for screening between Gaussian curvature and disclinations. In…
Variational principle for a solid in classical mechanics is formulated in terms of a thin elastic 4D bar strain in Minkowsky events space of special relativity. It is shown, that the sum of elastic 4-energies of weak twist and bending under…
Although fully elastic when static, granular media become transiently elastic when being slowly sheared -- during which both the elastic energy and stress relax. Starting from this observation, we cogently derive the framework for granular…
The relation between the elastic wave equation for plane, isotropic bodies and an underlying classical ray dynamics is investigated. We study in particular the eigenfrequencies of an elastic disc with free boundaries and their connection to…
This letter proposes a general dynamic formulation of slack bus. With this aim, the angle constraint imposed by the slack bus is redefined as a set of differential equations and an energy source. The existence and role of the transient…
Integral expressions are determined for the elastic displacement and stress fields due to stationary or moving dislocation loops in finite samples. These general expressions are valid for anisotropic media as well. Specifically for the…
The dynamic impedance of a sphere oscillating in an elastic medium is considered. Oestreicher's formula for the impedance of a sphere bonded to the surrounding medium can be expressed simply in terms of three lumped impedances associated…
The well known formulas express the curvature and the torsion of a curve in $R^3$ in terms of euclidean invariants of its derivatives. We obtain expressions of this kind for all curvatures of curves in $R^n$. It follows that a curve in…
Dynamics, the study of change, is normally the subject of mechanics. Whether the chosen mechanics is ``fundamental'' and deterministic or ``phenomenological'' and stochastic, all changes are described relative to an external time. Here we…
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…
The behaviour of elastic structures undergoing large deformations is the result of the competition between confining conditions, self-avoidance and elasticity. This combination of multiple phenomena creates a geometrical frustration that…
We investigate by exact optimization method properties of two- and three-dimensional systems of elastic lines in presence of splayed columnar disorder. The ground state of many lines is separable both in 2d and 3d leading to a random walk…
The viscoelasticity of two-dimensional liquids is quantified in an experiment using a dusty plasma. An experimental method is demonstrated for measuring the wavenumber-dependent viscosity, $\eta(k)$, which is a quantitative indicator of…