Advances in Mechanics and Mathematics pp 3-87 | Cite as
Dynamics of Rigid Bodies Systems with Unilateral or Frictional Constraints
Formulation And Well-Posedness
Chapter
- 6 Citations
- 301 Downloads
Abstract
The classical theory of rigid bodies systems dynamics is extended into two directions. First, systematic formulation of the dynamics of systems undergoing perfect unilateral constraints is derived. The general admissible form of the impact constitutive equation is obtained. Well-posedness of the evolution problem is proved under the assumption that the data are analytic. Second, systematic formulation of systems undergoing frictional bilateral constraints is discussed. Well-posedness of the associated evolution problem is also demonstrated.
Keywords
Analytical Dynamics Non-smooth Mechanics Impact FrictionPreview
Unable to display preview. Download preview PDF.
References
- [1]
- [2]P. Ballard (2000), The dynamics of discrete mechanical systems with perfect unilateral constraints, Archive for Rational Mechanics and Analysis, 154, pp 199–274.MathSciNetADSzbMATHCrossRefGoogle Scholar
- [3]A. Bressan (1960), Incompatibilità dei Teoremi di Esistenza e di Unicità del Moto per un Tipo molto Comune e Regolare di Sistemi Meccanici, Annali della Scuola Normale Superiore di Pisa, Serie III, Vol. XIV, pp 333348.Google Scholar
- [4]H. Brezis (1973), Opérateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert, North-Holland Publishing Company.Google Scholar
- [5]I. Chavel (1993), Riemannian Geometry: a Modern Introduction, Cambridge University Press.Google Scholar
- [6]E.A. Coddington and N. Levinson (1955), Theory of Ordinary Differential Equations, McGraw-Hill Book Company.Google Scholar
- [7]P. L Ötstedt (1981), Coulomb Friction in Two-Dimensional Rigid Body Systems, Z. Angew. Math. u. Mech., 61, pp 605–615.CrossRefGoogle Scholar
- [8]P. Lötstedt (1982), Mechanical Systems of Rigid Bodies subject to Unilateral Constraints, SIAM J. Appl. Math., 42, no 2, pp 281–296.MathSciNetzbMATHCrossRefGoogle Scholar
- [9]M.D.P. Monteiro Marques (1993), Differential Inclusions in Non-smooth Mechanical Problems, Birkhaüser Verlag, Basel-Boston-Berlin.Google Scholar
- [10]J.J. Moreau (1983), Standard inelastic shocks and the dynamics of unilateral constraints, in Unilateral problems in structural analysis ( G. Del Piero and F. Macen Eds), Springer-Verlag, Wien, New-York, pp 173–221.Google Scholar
- [11]J. J. Moreau (1988), Unilateral contact and dry friction in finite freedom dynamics, in Nonsmooth Mechanics and Applications, CISM Courses and Lectures No 302 ( J.J. Moreau and P.D. Panagiotopoulos Eds), Springer-Verlag, Wien, New-York, pp 1–82.Google Scholar
- [12]J.J. Moreau (1988), Bounded variation in time, in Topics in Non-smooth Mechanics ( J.J. Moreau, P.D. Panagiotopoulos, G. Strang, Eds.), Birkhaüser Verlag, Basel-Boston-Berlin, pp 1–74.Google Scholar
- [13]D. Percivale (1985), Uniqueness in the Elastic Bounce Problem, I, Journal of Differential Equations, 56, pp 206–215.MathSciNetzbMATHCrossRefGoogle Scholar
- [14]D. Percivale (1991), Uniqueness in the Elastic Bounce Problem, II, Journal of Differential Equations, 90, pp 304–315.MathSciNetzbMATHCrossRefGoogle Scholar
- [15]R.T. Rockafellar (1970), Convex Analysis, Princeton University Press.Google Scholar
- [16]W. Rudin (1966), Real and complex analysis, McGraw-Hill.Google Scholar
- [17]M. Schatzman (1978), A Class of Nonlinear Differential Equations of Second Order in Time, Nonlinear Analysis, Theory, Methods and Applications, 2, No 2, pp 355–373.MathSciNetzbMATHCrossRefGoogle Scholar
- [18]M. Schatzman (1998), Uniqueness and continuous dependence on data for one dimensional impact problems, Mathematical and Computational Modelling, 28, No. 4–8, pp 1–18.MathSciNetzbMATHCrossRefGoogle Scholar
Copyright information
© Springer Science+Business Media Dordrecht 2002