An overview of the formulation, existence and uniqueness issues for the initial value problem raised by the dynamics of discrete systems with unilateral contact and dry friction

Ballard, Patrick; Charles, Alexandre

doi:10.1016/j.crme.2017.12.010

Cited by 3 publications

(2 citation statements)

References 19 publications

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“…where 𝜇 > 0 is the friction coefficient, and 𝑁 (𝑡) is the magnitude of the force normal to the surface. As discussed in Moreau [12], Ballard and Charles [3], we may write this compactly as…”

Section: Counterexamplementioning

confidence: 99%

“…Contact and impact are typically modelled with unilateral constraints: inequalities involving the coordinates of some bodies, which are satisfied when those bodies do not interpenetrate. Such constraints are essential components of models of robots [7,10] and other systems [6], and it is natural to enquire about the existence and uniqueness of solutions to initial value problems for such models [3]. In the 1960s, it was discovered that the motion of a unilaterally constrained particle acted on by an external force is in general non-unique, even if the force is an infinitely differentiable function of time [1,4,14].…”

Section: Introductionmentioning

confidence: 99%

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A counterexample to analyticity in frictional dynamics

Dance¹

2022

ESAIM: M2AN

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We consider the motion of a particle acted on by dry friction and a force that is an analytic function of time. We give a counterexample to the claim that such motions are given by analytic functions of time. Several published arguments concerning existence and uniqueness in unilateral dynamics with friction rely on the analyticity of such motions. The counterexample invalidates those arguments for motions in three or more dimensions.

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Section: Counterexamplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A counterexample to analyticity in frictional dynamics

Dance¹

2022

ESAIM: M2AN

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A catching-up algorithm for multibody dynamics with impacts and dry friction

Charles

Casenave

Glocker

2018

Computer Methods in Applied Mechanics and Engineering

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Existence and uniqueness of the motion of a particle subject to a unilateral constraint and friction

Dance

2024

ESAIM: M2AN

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We prove that there exists a unique solution to the initial value problem describing the motion of a particle subject to a unilateral constraint and Coulomb friction, if the external force acting on the particle is an analytic function of time and of the particle’s position and velocity. Previous work claimed that this problem has a local series solution that corresponds to an analytic function, after any impacts have been resolved. However, a counterexample to that claim was recently discovered, involving a particle starting to slide, in which the series solution is divergent, and thus does not correspond to an analytic function. This paper corrects previous arguments by considering a general formal series solution for a particle that is starting to slide.

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An overview of the formulation, existence and uniqueness issues for the initial value problem raised by the dynamics of discrete systems with unilateral contact and dry friction

Cited by 3 publications

References 19 publications

A counterexample to analyticity in frictional dynamics

A counterexample to analyticity in frictional dynamics

A catching-up algorithm for multibody dynamics with impacts and dry friction

Existence and uniqueness of the motion of a particle subject to a unilateral constraint and friction

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