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Flexible Multibody Dynamics Formulation by Hamilton’s Equations

[+] Author Affiliations
Martin M. Tong

The Aerospace Corporation, El Segundo, CA

Paper No. IMECE2010-39727, pp. 725-734; 10 pages
  • ASME 2010 International Mechanical Engineering Congress and Exposition
  • Volume 8: Dynamic Systems and Control, Parts A and B
  • Vancouver, British Columbia, Canada, November 12–18, 2010
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-4445-8
  • Copyright © 2010 by ASME


Numerical solution of the dynamics equations of a flexible multibody system as represented by Hamilton’s canonical equations requires that its generalized velocities be solved from the generalized momenta p. The relation between them is p = J(q), where J is the system mass matrix and q is the generalized coordinates. This paper presents the dynamics equations for a generic flexible multibody system as represented by and gives emphasis to a systematic way of constructing the matrix J for solving . The mass matrix is shown to be separable into four submatrices Jrr , Jrf , Jfr and Jff relating the joint momenta and flexible body mementa to the joint coordinate rates and the flexible body deformation coordinate rates. Explicit formulas are given for these submatrices. The equations of motion presented here lend insight to the structure of the flexible multibody dynamics equations. They are also a versatile alternative to the acceleration-based dynamics equations for modeling mechanical systems.

Copyright © 2010 by ASME



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