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.
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References
R. Abraham and J.E. Marsden (1985), Foundations of Mechanics, Addison-Wesley.
P. Ballard (2000), The dynamics of discrete mechanical systems with perfect unilateral constraints, Archive for Rational Mechanics and Analysis, 154, pp 199–274.
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.
H. Brezis (1973), Opérateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert, North-Holland Publishing Company.
I. Chavel (1993), Riemannian Geometry: a Modern Introduction, Cambridge University Press.
E.A. Coddington and N. Levinson (1955), Theory of Ordinary Differential Equations, McGraw-Hill Book Company.
P. L Ötstedt (1981), Coulomb Friction in Two-Dimensional Rigid Body Systems, Z. Angew. Math. u. Mech., 61, pp 605–615.
P. Lötstedt (1982), Mechanical Systems of Rigid Bodies subject to Unilateral Constraints, SIAM J. Appl. Math., 42, no 2, pp 281–296.
M.D.P. Monteiro Marques (1993), Differential Inclusions in Non-smooth Mechanical Problems, Birkhaüser Verlag, Basel-Boston-Berlin.
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.
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.
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.
D. Percivale (1985), Uniqueness in the Elastic Bounce Problem, I, Journal of Differential Equations, 56, pp 206–215.
D. Percivale (1991), Uniqueness in the Elastic Bounce Problem, II, Journal of Differential Equations, 90, pp 304–315.
R.T. Rockafellar (1970), Convex Analysis, Princeton University Press.
W. Rudin (1966), Real and complex analysis, McGraw-Hill.
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.
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.
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Ballard, P. (2002). Dynamics of Rigid Bodies Systems with Unilateral or Frictional Constraints. In: Gao, D.Y., Ogden, R.W. (eds) Advances in Mechanics and Mathematics. Advances in Mechanics and Mathematics, vol 1. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-4435-4_1
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DOI: https://doi.org/10.1007/978-1-4757-4435-4_1
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