Journal ArticleDOI
Analytical Mechanics. Addendum I: Inequality Constraints with Elastic Impacts. The Convex Case
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In this paper, it was shown that the theorem of stationary action still holds as an inequality and that the variation of the unknown impact time implies new variational expressions in inequality form for the impact problem.Abstract:
The aim of the present paper is to present some new results in Analytical Mechanics when impacts may occur We prove certain equivalent forms for d'Alembert's principle including the velocity discontinuity, and then we show that the theorem of stationary action still holds as an inequality The consideration of the variation of the unknown impact time implies certain new variational expressions in inequality form for the impact problemread more
Citations
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Ghosts and machines : regularized variational methods for interactive simulations of multibodies with dry frictional contacts
TL;DR: In this article, a time-discrete formulation of the variational principle of mechanics is used to provide a consistent theoretical framework for the construction and analysis of low-order integration methods.
Journal ArticleDOI
Hamilton’s Principle as Variational Inequality for Mechanical Systems with Impact
TL;DR: The principle of Hamilton with strong variations is valid forperfect unilateral constraints with a completely elastic impact law, whereas the weak form of Hamilton’s principle only requires perfect unilateral constraints and no condition on the energy.
Journal ArticleDOI
Inequality constraints with elastic impacts in deformable bodies. The convex case
TL;DR: In this article, it was shown that the theorem of stationary action still holds as an inequality for the impact problem and that the variation of the unknown impact time implies new variational expressions in inequality form.
Journal ArticleDOI
Augmented Perpetual Manifolds and Perpetual Mechanical Systems—Part I: Definitions, Theorem, and Corollary for Triggering Perpetual Manifolds, Application in Reduced-Order Modeling and Particle-Wave Motion of Flexible Mechanical Systems
TL;DR: In this article, the authors extended the definition of perpetual manifolds to the augmented perpetual manifold of rigid body motions and proved that for harmonic motion, the system moves in dual mode as wave-particle.
Journal ArticleDOI
Analysis of Discrete Mechanical Systems With Blockable Directions
TL;DR: In this article, an impulsive action integral is proposed for the sudden introduction of bilateral constraints into a mechanical process and its sudden removal is releasing, where the projectors of the tangent space of the submanifold and the cotangent space are derived.
References
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Book
An introduction to variational inequalities and their applications
TL;DR: In this paper, the SIAM edition Preface Glossary of notations Introduction Part I. Variational Inequalities in Rn Part II. Free Boundary Problems Governed by Elliptic Equations and Systems Part VII. A One Phase Stefan Problem Bibliography Index.
MonographDOI
Multibody dynamics with unilateral contacts
TL;DR: Unilateral Contact - Problem Formulation (A. Curnier).- Scalar Force Potentials in Rigid Multibody Systems (Ch. Glocker).
Book ChapterDOI
Unilateral Contact and Dry Friction in Finite Freedom Dynamics
TL;DR: In this article, an approach to the dynamics of mechanical systems with a finite number of degrees of freedom, involving unilateral constraints, is developed, where the velocity is not supposed to be a differentiable function of time, but only to have locally bounded variation.