Comparison of solution strategies for multibody dynamics equations

International Journal for Numerical Methods in Engineering

Volumn 88, Issue 7, 2011, Pages 637-656

  Mariti, L ^a   Belfiore, N P ^b   Pennestri E ^a   Valentini, P P ^a  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

DAE system; Multibody dynamics; Numerical methods

Indexed keywords

ABSOLUTE COORDINATE; CARTESIAN COORDINATE; COMMERCIAL SOFTWARE; CONSTRAINT EQUATION; DAE SYSTEMS; LEAST SQUARE; MULTI BODY SYSTEMS; MULTI-BODY DYNAMIC; ORTHOGONALIZATION; PSEUDO-INVERSES; REAL-TIME COMPUTATIONS; REDUNDANT COORDINATES; REFERENCE POINTS; SOLUTION STRATEGY; TEST CASE;

COMPUTATIONAL EFFICIENCY;

LEAST SQUARES APPROXIMATIONS;

EID: 80054092032     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.3190     Document Type: Article

References (36)

1. Unda J, de Jalon JG, Losantos F, Emparantza R. A comparative study of different formulations of the dynamic equations of constrained mechanical systems. ASME Journal of Mechanisms, Transmissions, and Automation in Design 1987; 109:466-474.
2. Erberhard P, Schielen W. Computational dynamics of multibody systems: history, formalisms, and applications. ASME Journal of Computational and Nonlinear Dynamics 2006; 1:3-12.
3. Bauchau O, Laulusa A. Review of classical approaches for constraints enforcement in multibody systems. Journal of Computational and Non Linear Dynamics 2008; 3:1-8.
4. Laulusa A, Bauchau OA. Review of classical approaches for constraint enforcement in multibody systems. Journal of Computational and Nonlinear Dynamics 2008; 3. http://dx.doi.org/10.1115/1.2803257.
5. Wehage RA, Haug EJ. Generalized coordinate partitioning for dimension reduction in analysis of constrained dynamic systems. ASME Journal of Mechanical Design 1982; 134:247-255.
6. Haug EJ. Computer-aided Kinematics and Dynamics of Mechanical Systems. Allyn and Bacon: Newton, MA, 1989.
7. Haug EJ, Yen J. Generalized coordinate partitioning methods for numerical integration of differential-algebraic equations of dynamics. In Real-time Integration Methods for Mechanical System Simulation, Haug EJ, Deyo RC (eds), NATO ASI Series, vol. 69. Springer: Berlin, 1991; 97-114.
8. Walton EC, Steeves WC. A new matrix theorem and its application for establishing independent coordinates for complex dynamical systems with constraints. NASA Technical Report TR-327, NASA, 1969.
9. Mani NK, Haug EJ, Atkinson KE. Singular value decomposition for analysis of mechanical system dynamics. ASME Journal of Mechanisms, Transmissions, and Automation in Design 1985; 107:82-87.
10. Kim SS, Vanderploeg MJ. QR decomposition for state space representation of constrained mechanical dynamic systems. ASME Journal of Mechanisms, Transmissions, and Automation in Design 1986; 108:176-182.
11. Amirouche FML, Ider SK. Coordinate reduction in the dynamics of constrained multibody systems-a new approach. ASME Journal of Applied Mechanics 1988; 55:899-904.
12. Wang JT, Huston RL. Computational methods in constrained multibody dynamics: matrix formalisms. Computers and Structures 1988; 29:331-338.
13. Wang JT, Huston RL. A comparison of analysis methods of redundant multibody systems. Mechanics Research Communications 1989; 16:175-182.
14. Pennestrì E, Valentini PP. Coordinate reduction strategies in multibody dynamics: a review. Proceedings of the Conference on Multibody System Dynamics, London, 2007.
15. Udwadia FE, Kalaba RE. Analytical Dynamics a New Approach. Cambridge University Press: Cambridge, 1996.
16. Udwadia FE, Phohomsiri P. Explicit equations of motion for constrained mechanical systems with singular mass matrices and applications to multi-body dynamics. Proceedings of the Royal Society, Series A 2006; 462:2097-2117.
17. Pennestrì E, Vita L, de Falco D. An investigation of the influence of pseudoinverse matrix calculations on multibody dynamics simulations by means of the Udwadia-Kalaba formulation. Journal of Aerospace Engineering 2008; 22:365-372.
18. Vlasenko D, Kasper R. Implementation of consequent stabilization method for simulation of multibodies described in absolute coordinates. Multibody System Dynamics 2009; 22:297-315.
19. Maggi GA. Di alcune nuove forme della dinamica applicabili ai sistemi anolonomi. Rendiconti della Regia Accademia dei Lincei-Serie V 1901; X:287-291.
20. Borri M, Bottasso CL, Mantegazza P. Equivalence of Kane's and Maggi's equations. Meccanica 1990; 25:272-274.
21. Kurdila A, Papastravidis JG. Kamat MP. Role of Maggi's equations in computational methods for constrained multibody systems. Journal of Guidance, Control, and Dynamics 1990; 13:113-120.
22. Eich-Soellner E, Führer C. Numerical Methods in Multibody Dynamics. B.G. Teubner: Stuttgart, 1998.
23. Pennestrì E, Valentini PP, Vita L. Multibody dynamics simulation of planar linkages with Dahl friction. Multibody System Dynamics 2007; 17:321-347.
24. Nikravesh PE. Initial condition correction in multibody dynamics. Multibody System Dynamics 2007; 18:107-115.
25. Shabana AA. Computational Dynamics. Wiley: New York, 1994.
26. Amirouche F. Fundamentals of Multibody Dynamics. Birkhhäuser: Basel, 2004.
27. Kamman RL, Huston JW. Dynamics of constrained multibody systems. ASME Journal of Applied Mechanics 1985; 51:899-903.
28. Singh RP, Likins PW. Singular value decomposition for constrained mechanical systems. ASME Journal of Applied Mechanics 1985; 52:943-948.
29. Golub G, van Loan C. Matrix Computations (3rd edn). The Johns Hopkins University Press: London, 1996.
30. Arabyan A, Wu F. An improved formulation for constrained mechanical systems. Multibody System Dynamics 1998; 2:49-69.
31. Baumgarte JW. Stabilization of constraints and integrals of motion in dynamical systems. Computer Methods in Applied Mechanics and Engineering 1972; 1:1-16.
32. Baumgarte JW. A new method of stabilization for holonomic constraints. ASME Journal of Applied Mechanics 1983; 50:869-870.
33. Udwadia FE, Kalaba R. Explicit equations of motion for mechanical systems with nonideal constraints. ASME Journal of Applied Mechanics 2001; 68:462-467.
34. Campbell SL. Generalized Inverses of Linear Transformations. Dover Publications, Inc.: New York, 1979.
35. Cheli F, Pennestrì E. Cinematica e Dinamica dei Sistemi Multibody, vol. 1. Casa Editrice Ambrosiana: Milano, 2006.
36. Shabana AA. Dynamics of Multibody Systems. Wiley: New York, 1989.