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Exact Linearization of Multibody Systems Using User-defined Coordinates
Technical Paper
2006-01-0587
ISSN: 0148-7191, e-ISSN: 2688-3627
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English
Abstract
An exact approach to linearize the equations of motion of multibody systems is presented. The method has general applicability and it is well suited to linearize the index-3 Differential Algebraic Equations (DAE) governing the state of a dynamical system. Moreover, the method was extended to linearize a dynamical system in terms of user-defined coordinates without the need to reformulate the governing equations; this feature is of particular interest in disciplines like rotordynamics where eigensolutions are requested in terms of coordinates defined in a rotating frame.
Contrary to other linearization methods, the proposed approach implements a closed-form computation of the linearized equations of motion; all second order effects are taken into account and no numerical differentiation is required. The proposed method inflates the governing equations and then computes a set of sensitivities that provide the linearization of interest. The method is attractive because (a) it handles large heterogeneous problems, (b) it optionally linearizes a system in terms of user-defined coordinates, (c) it can be optimized using parallel algorithms, and (d) it provides a straightforward implementation in a general-purpose dynamics simulation code such as MSC.ADAMS.
Authors
Citation
Ortiz, J. and Negrut, D., "Exact Linearization of Multibody Systems Using User-defined Coordinates," SAE Technical Paper 2006-01-0587, 2006, https://doi.org/10.4271/2006-01-0587.Also In
SAE 2006 Transactions Journal of Passenger Cars: Mechanical Systems
Number: V115-6; Published: 2007-03-30
Number: V115-6; Published: 2007-03-30
References
- Anderson K.S. Duan S. Highly parallelizable low order dynamics algorithm for complex multi-rigid-body systems AIAA Journal of Guidance, Control and Dynamics 23 2 2000
- Ascher U. M. Petzold L. R. Computer Methods for Ordinary Differential Equations and Differential Algebraic Equations SIAM Philadelphia, PA 1998
- de Jalon J. Garcia Bayo E. Kinematic and Dynamic Simulation of Multibody Systems The Real-Time Challenge Springer-Verlag Berlin 11994
- Featherstone R. The calculation of robot dynamics using articulated-body inertias International Journal of Robotics Research 1 13 30 1983
- Haug E. J. Computer-Aided Kinematics and Dynamics of Mechanical Systems Prentice-Hall Englewood Cliffs, New Jersey 1989
- Johnson W. Helicopter Theory Dover Publications, Inc. New York 1980
- MSCsoftware. ADAMS User Manual 2005
- Negrut D. Ortiz J. L. On an approach for the linearization of the differential algebraic equations of multibody dynamics (detc2005-8510) Proceeding of the 2005 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications 2005
- Wilkie W.K. Mirick P.H. Langston C.W. Rotating shake test and modal analysis of a model helicopter rotor blade Computing Science Technical Report NASA Technical Memorandum 4760 Vehicle Technology Center, U.S. Army Research Laboratory, Langley Research Center Hampton, Virginia 1997