Die vorliegende Arbeit behandelt die Berechnung der Beschleunigungen in starren Mehrkorpersystemen, wenn diese dem Einflus mengenwertiger Kraftgesetze ausgesetzt sind. Die Kraftgesetze werden uber nicht-glatte Potentialfunktionen berucksichtigt und uber deren generalisiertes Differential dargestellt. Die dadurch entstehenden Punkt-Mengen-Abbildungen beinhalten neben glatten Kraftkennlinien auch Krafte aus zweiseitigen Bindungen sowie Kombinationen aus beiden wie einseitige Bindungen, Trockenreibung oder vorgespannte Federn mit Spiel. Stose werden nicht behandelt. Die klassischen Prinzipe von d'Alembert, Jourdain und Gauss werden mit Hilfe variationeller Ungleichungen verallgemeinert. Es wird ein streng konvexes Minimierungsproblem fur die unbekannten Beschleunigungen des Systems aufgestellt, das in der klassischen Mechanik als das Prinzip des kleinsten Zwangs bekannt ist.



The paper treats the evaluation of the accelerations in rigid multibody systems which are subjected to set-valued force interactions. The interaction laws may be represented by non-smooth potential functions, and then derived through generalized differentiation. The resulting multifunctions contain the cases of smooth force characteristics, bilateral constraints, as well as combinations of them like unilateral constraints, dry friction, or prestressed springs with play. Impacts are excluded. A generalization of the classical principles of d'Alembert, Jourdain, and Gauss in terms of variational inequalities will be given. A strictly convex minimization problem depending on the unknown accelerations of the system will be stated, known in classical mechanics as the Principle of Least Constraints.

/pdf/the-principles-of-d-alembert-jourdain-and-gauss-in-nonsmooth-dbj7bu2m4d.pdf

The Principles of d'Alembert, Jourdain, and Gauss in Nonsmooth Dynamics Part I: Scleronomic Multibody Systems

The paper treats the evaluation of the accelerations in rigid multibody systems which are subjected to displacement dependent setvalued force interactions. The interaction laws are represented by nonsmooth displacement potentials and derived through generalized differentiation. The resulting multifunctions contain the cases of smooth force characteristics, bilateral constraints, as well as combinations of them like unilateral constraints or prestressed springs with play. Impacts are excluded. A generalization of the classical principles of d’Alembert, Jourdain, and Gauss in terms of hemi-variational inequalities is given. A strictly convex minimization problem depending on the unknown accelerations is stated, known in classical mechanics as the Principle of Least Constraints. The theory is applied to unilaterally constrained systems.

/pdf/displacement-potentials-in-non-smooth-dynamics-gqcf52vz0i.pdf

Displacement Potentials in Non-Smooth Dynamics

The aim of this paper is to examine unilateral constraints in analytical mechanics. Examples of mechanical systems subject to unilateral constraints are moving rigid bodies which may enter into contact and detach from each other. But unilateral constraints also occur when two satellites are connected by a rope.

Generalized Variational Principles and Unilateral Constraints in Analytical Mechanics

The present paper deals with Jourdain's principle for unilateral constraints, depending on the velocities, written as a hemivariational inequality, so that it is possible to treat very general constraints. The difference from bilateral restrictions is discussed, and it is shown why it is not possible to describe rigid unilateral contraints with the help of the hemivariational inequality expressing Jourdain's principle.

Jourdain's principle for unilateral constrains

The present paper deals with variational principles in terms of hemivariational inequalities and with differential inclusions for unilateral constraints in analytical mechanics. It is discussed how it is possible to describe one-sided constraints in a very general manner by the help of Clarke's generalized gradient.

https://link.springer.com/content/pdf/10.1007/BF01556329.pdf

P. D. Panagiotopoulous

Papers

F. H. Clarke's Generalized Gradient and Fourier's Principle