Inertial couplings between unilateral and bilateral holonomic constraints in frictionless Lagrangian systems
In this paper, the following problem is analyzed: Given a frictionless Lagrangian system subject to complementarity relations (due to a set of unilateral constraints) that define a linear complementarity problem whose matrix is the so-called Delassus’ matrix, study the influence of a set of bilatera...
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| Published in | Multibody system dynamics Vol. 29; no. 3; pp. 289 - 325 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Dordrecht
Springer Netherlands
01.03.2013
Springer Verlag |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1384-5640 1573-272X |
| DOI | 10.1007/s11044-012-9317-8 |
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| Abstract | In this paper, the following problem is analyzed: Given a frictionless Lagrangian system subject to complementarity relations (due to a set of unilateral constraints) that define a linear complementarity problem whose matrix is the so-called Delassus’ matrix, study the influence of a set of bilateral constraints added to the dynamics on the Delassus’ matrix. Two main paths are followed: the Lagrange multipliers method and the reduced coordinates method. The link with optimization (the Gauss’ principle of mechanics) and the case of impacts, are also examined. The kinetic angles between the bilateral and the unilateral constraints are used to study the definiteness of the Delassus’ matrix. |
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| AbstractList | In this paper, the following problem is analyzed: Given a frictionless Lagrangian system subject to complementarity relations (due to a set of unilateral constraints) that define a linear complementarity problem whose matrix is the so-called Delassus' matrix, study the influence of a set of bilateral constraints added to the dynamics on the Delassus' matrix. Two main paths are followed: the Lagrange multipliers method and the reduced coordinates method. The link with optimization (the Gauss' principle of mechanics) and the case of impacts, are also examined. The kinetic angles between the bilateral and the unilateral constraints are used to study the definiteness of the Delassus' matrix. |
| Author | Brogliato, Bernard |
| Author_xml | – sequence: 1 givenname: Bernard surname: Brogliato fullname: Brogliato, Bernard email: bernard.brogliato@inria.fr organization: Bipop team-project, ZIRST Montbonnot, INRIA |
| BackLink | https://inria.hal.science/hal-00825581$$DView record in HAL |
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| Cites_doi | 10.1007/978-3-662-04800-9 10.1007/s002050000105 10.1023/A:1019581227898 10.1007/978-3-540-44398-8 10.1007/0-387-29195-4_16 10.1007/s00707-004-0076-3 10.1016/0362-546X(78)90022-6 10.1016/S0997-7538(98)80007-7 10.1142/S0218202505003873 10.1007/s11071-009-9484-1 10.1137/0142022 10.1515/9781400873173 10.1007/s11044-006-9028-0 10.1007/978-3-642-01100-9 10.1023/A:1012084517966 10.1007/978-3-642-56468-0 10.1016/j.euromechsol.2006.07.002 10.1109/9.1220 10.1002/9783527618385 10.1023/A:1023321630764 10.1007/s00205-010-0311-0 10.1051/m2an/1993270606731 10.1007/s11071-007-9244-z 10.1137/0304014 10.1016/j.jde.2010.10.010 10.1016/S0997-7538(99)00144-8 10.1007/978-3-540-76975-0 10.1007/978-3-0348-7614-8 10.1007/978-3-540-75392-6 10.1007/978-3-7091-2624-0_1 10.1017/CBO9780511626432 10.1007/978-1-4471-0557-2 10.1112/jlms/s1-43.1.378 10.1023/A:1024567523268 10.1007/s11071-011-0094-3 10.1007/978-3-211-48243-8_2 10.1007/978-3-540-44479-4 |
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| Issue | 3 |
| Keywords | Solid mechanics Impact Singularity Gauss’ principle Multibody systems Kinetic angle Linear complementarity problem Reduced coordinates Delassus’ matrix Lagrange multiplier Bilateral constraints Unilateral constraints Lagrangian system Gauss' principle Delassus' matrix |
| Language | English |
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| References_xml | – reference: LancasterP.TismenetskyM.The Theory of Matrices19852New YorkAcademic Press0558.15001 – reference: GlockerC.HaslingerJ.StavroulakisG.An introduction to impactsNonsmooth Mechanics of Solids2006New YorkSpringer4510210.1007/978-3-211-48243-8_2 – reference: Monteiro MarquesM.D.P.Differential Inclusions in Non-smooth Mechanical Problems: Shocks and Dry Friction1993BostonBirkhäuser – reference: ArponenT.Regularization of constraint singularities in multibody systemsMultibody Syst. Dyn.2001635537518719591018.7000210.1023/A:1012084517966 – reference: Hiriart-UrrutyJ.B.LemaréchalC.Fundamentals of Convex Analysis2001BerlinSpringer0998.4900110.1007/978-3-642-56468-0 – reference: PaoliL.SchatzmanM.Mouvement à nombre fini de degrés de liberté avec contraintes unilatérales: cas avec perte d’énergieModèl. Math. Anal. Numér.199327667371712469950792.34012 – reference: BlajerW.Augmented Lagrangian formulation: geometrical interpretation and application to systems with singularities and redundancyMultibody Syst. Dyn.2002814115919050911022.7000410.1023/A:1019581227898 – reference: DelassusE.Mémoire sur la théorie des liaisons finies unilatéralesAnn. Sci. Ec. Norm. Super., Ser. 3191734951791509203JFM 46.1178.01 – reference: LeineR.I.van de WouwN.Stability and Convergence of Mechanical Systems with Unilateral Constraints2008BerlinSpringer1143.7000110.1007/978-3-540-76975-0 – reference: MangasarianO.L.Nonlinear Programming1969New YorkMcGraw-Hill0194.20201 – reference: MüllerA.A conservative elimination procedure for permanently redundant closure constraints in MBS-models with relative coordinatesMultibody Syst. Dyn.20061630933022873671119.7000610.1007/s11044-006-9028-0 – reference: StuderC.Numerics of Unilateral Contacts and Friction: Modeling and Numerical Time Integration in Non-smooth Dynamics2009BerlinSpringer1162.7000210.1007/978-3-642-01100-9 – reference: BallardP.The dynamics of discrete mechanical systems with perfect unilateral constraintsArch. Ration. Mech. Anal.2000154319927417854730965.7002410.1007/s002050000105 – reference: DzonouR.Monteiro MarquesM.D.P.PaoliL.A convergence result for a vibro-impact problem with a general inertia operatorNonlinear Dyn.2009581–236138425508201183.7005910.1007/s11071-009-9484-1 – reference: AcaryV.BrogliatoB.Numerical Methods for Nonsmooth Dynamical Systems2008BerlinSpringer1173.74001 – reference: OrY.RimonE.Investigation of Painlevé’s paradox and dynamic jamming during mechanism sliding motionNonlinear Dyn.2012672164716680605790310.1007/s11071-011-0094-3 – reference: LeineR.I.NijmeijerH.Dynamics and Bifurcations of Non-smooth Mechanical Systems2004BerlinSpringer1068.70003 – reference: MoreauJ.J.Les liaisons unilatérales et le principe de GaussC. R. Acad. Sci. Paris19632564871874175342 – reference: BrogliatoB.Nonsmooth Mechanics19992LondonSpringer0917.7300210.1007/978-1-4471-0557-2 – reference: PaoliL.A proximal-like method for a class of second order measure-differential inclusions describing vibro-impact problemsJ. Differ. Equ.201125047651427378510583424310.1016/j.jde.2010.10.010 – reference: LötstedtP.Mechanical systems of rigid bodies subject to unilateral constraintsSIAM J. Appl. Math.19824222812966502240489.7001610.1137/0142022 – reference: FrémondM.Non-smooth Thermomechanics2002BerlinSpringer0990.8000110.1007/978-3-662-04800-9 – reference: BernsteinD.S.Matrix, Mathematics. Theory, Facts, and Formulas with Application to Linear Systems Theory2005PrincetonPrinceton University Press1075.15001 – reference: GlockerC.AeberhardU.AlartP.MaisonneuveO.RockafellarR.T.The geometry of Newton’s cradleNonsmooth Mechanics and Analysis. 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| Snippet | In this paper, the following problem is analyzed: Given a frictionless Lagrangian system subject to complementarity relations (due to a set of unilateral... |
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| SubjectTerms | Automotive Engineering Control Dynamical Systems Electrical Engineering Engineering Mathematics Mechanical Engineering Optimization Optimization and Control Vibration |
| Title | Inertial couplings between unilateral and bilateral holonomic constraints in frictionless Lagrangian systems |
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