Related papers: An elementary approach based on variational inequa…

We outline a phenomenological model to assess friction at the interface between two bodies in mutual contact. Although the approach is general, the application inspiring the approach is the Discrete Element Method. The kinematics of the…

The problem of the existence and uniqueness of the motion of the system of an arbitrary number linear oscillators under a generalized dry-friction type control is studied. This type of control arises in the problem of steering the system to…

We introduce a family of proximal discontinuous Galerkin methods for variational inequalities, focusing on the obstacle problem as a didactic example. Each member of this family is born from applying a different well-known nonconforming…

Rectilinear crawling locomotion is a primitive and common mode of locomotion in slender, soft-bodied animals. It requires coordinated contractions that propagate along a body that interacts frictionally with its environment. We propose a…

Many applications of contemporary science involve multiscale dynamics, which are typically characterized by the time and space scale separation of patterns of motion, with fewer slowly evolving variables and much larger set of faster…

The purpose of this paper is to illustrate, in an experimental facility consisting of a simple pendular device, the performance of a sliding mode adaptive position-feedback tracking controller of mechanical systems with friction reported in…

This work introduces a new approach to velocity averaging lemmas in kinetic theory. This approach -- based upon the classical energy method -- provides a powerful duality principle in kinetic transport equations which allows for a natural…

Discrete mechanics is presented as an alternative to the equations of fluid mechanics, in particular to the Navier-Stokes equation. The derivation of the discrete equation of motion is built from the intuitions of Galileo, the principles of…

Bipedal locomotion is a phenomenon that still eludes a fundamental and concise mathematical understanding. Conceptual models that capture some relevant aspects of the process exist but their full explanatory power is not yet exhausted. In…

The simple realistic model of the tippe top is considered. An averaged system of equations of motion is obtained in special evolutionary variables. Through the qualitative analysis of this system the general features of the motion of the…

Force-based models describe pedestrian dynamics in analogy to classical mechanics by a system of second order ordinary differential equations. By investigating the linear stability of two main classes of forces, parameter regions with…

We propose a comprehensive framework for solving constrained variational inequalities via various classes of evolution equations displaying multi-scale aspects. In an infinite-dimensional Hilbertian framework, the class of dynamical systems…

We study the possibility of efficient intermittent locomotion for two-link bodies that slide by changing their interlink angle periodically in time. We find that the anisotropy ratio of the sliding friction coefficients is a key parameter,…

We consider the velocity fluctuations of a system of particles described by the Inelastic Maxwell Model. The present work extends the methods, previously employed to obtain the one-particle velocity distribution function, to the study of…

We study step-wise time approximations of non-linear hyperbolic initial value problems. The technique used here is a generalization of the minimizing movements method, using two time-scales: one for velocity, the other (potentially much…

Friction, the resistive force between two surfaces sliding past each other, is at the core of a wide diversity of locomotion schemes. While such schemes are somewhat understood for homogeneous environments, locomotion based on friction in…

A simple bilevel variational problem where the lower level is a variational inequality while the upper level is an optimization problem is studied. We consider an inexact version of the lower problem, which guarantees enough regularity to…

We study three different experiments that involve dry friction and periodic driving, and which employ both single and many-particle systems. These experimental set-ups, besides providing a playground for investigation of frictional effects,…

This paper presents a novel approach to numerically describe the interactions between rigid bodies, with a special focus on robotic grasping. Some of the more common approaches used to address such issues rely on satisfaction of a set of…

A finite element approach to the elastic flow of a curve coupled with a diffusion equation on the curve is analysed. Considering the graph case, the problem is weakly formulated and approximated with continuous linear finite elements, which…