Singular mass matrix and redundant constraints in unilaterally constrained Lagrangian and Hamiltonian systems

Bernard Brogliato 1 Daniel Goeleven 2, 3
1 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
2 PIMENT - Physique et Ingénierie Mathématique pour l'Énergie, l'environnemeNt et le bâtimenT
3 IREMIA - Institut de REcherche en Mathématiques et Informatique Appliquées
Abstract : This article deals with the analysis of the contact complementarity problem for Lagrangian systems subjected to unilateral constraints, and with a singular mass matrix and redundant constraints. Previous results by the authors on existence and uniqueness of solutions of some classes of variational inequalities are used to characterize the well-posedness of the contact problem. Criteria involving conditions on the tangent cone and the constraints gradient are given. It is shown that the proposed criteria easily extend to the case where the system is also subjected to a set of bilateral holonomic constraints, in addition to the unilateral ones. In the second part, it is shown how basic convex analysis may be used to show the equivalence between the Lagrangian and the Hamiltonian formalisms when the mass matrix is singular.
Keywords : Convex analysis Recession cone Singular Hamiltonian system Singular Lagrangian system Unilateral constraint Bilateral holonomic constraint Complementarity conditions Mixed linear complementarity problem Redundant constraints Legendre-Fenchel transformation
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Article dans une revue
Multibody System Dynamics, Springer Verlag, 2015, 35 (1), pp.39-61. 〈10.1007/s11044-014-9437-4〉
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Bernard Brogliato, Daniel Goeleven. Singular mass matrix and redundant constraints in unilaterally constrained Lagrangian and Hamiltonian systems. Multibody System Dynamics, Springer Verlag, 2015, 35 (1), pp.39-61. 〈10.1007/s11044-014-9437-4〉. 〈hal-01088286〉

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