Abstract
The classical theory of rigid bodies systems undergoing perfect bilateral constraints has received firm mathematical foundations for a long time. We extend it to the case where there are perfect unilateral constraints also. The formulation follows the line initiated by Schatzman (1978) and Moreau (1983). We give a parametrization-free formulation and try to identify the most general form of impact constitutive equation which is compatible with well-posedness. Then, well-posedness is proved under the assumption of analyticity of the data, since it is known, thanks to Bressan (1960) and Schatzman (1978), that uniqueness does not hold in the C ∞ setting.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ballard, P. (2000) The dynamics of discrete mechanical systems with perfect unilateral constraints, Archive for Rational Mechanics and Analysis 154, 199–274.
Ballard, P. (2001) Formulation and well-posedness of the dynamics of rigid bodies systems with perfect unilateral constraints, Philosophical Transactions of the Royal Society Serie A (to apppear).
Bressan, A. (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, 333–348.
Lötstedt, P. (1982), Mechanical systems of rigid bodies subject to unilateral constraints SIAM J. Appl. Math. 42, no 2, pp 281–296.
Moreau, J.J. (1983) Standard inelastic shocks and the dynamics of unilateral constraints, in Unilateral problems in structural analysis (G. Del Piero and F. Maceri Eds), Springer-Verlag, Wien, New-York, 173–221.
Percivale, D. (1985) Uniqueness in the elastic bounce problem, I, Journal of Differential Equations 56, 206–215.
Schatzman, M. (1978) A class of nonlinear differential equations of second order in time, Nonlinear Analysis, Theory, Methods é9 Applications 2, No 2, 355–373.
Schatzman, M. (1998) Uniqueness and continuous dependence on data for one dimen- sional impact problems, Mathematical and Computational Modelling 28, No. 4–8, 1–18.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Ballard, P. (2002). Formulation and Well-Posedness of Unilateral Multibody Dynamics. In: Contact Mechanics. Solid Mechanics and Its Applications, vol 103. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1154-8_3
Download citation
DOI: https://doi.org/10.1007/978-94-017-1154-8_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6099-0
Online ISBN: 978-94-017-1154-8
eBook Packages: Springer Book Archive