A Lagrangian multibody code for deriving the symbolic state-space equations of motion for open-loop systems containing flexible beams

David I.M. Forehand, Raya Khanin, Matthew P. Cartmell

Research output: Contribution to journalArticle

6 Citations (Scopus)


In this study, the development of a symbolic multibody code is described. This code uses Lagrange’s equations to derive automatically the state-space equations of motion, in relative coordinates, for open-loop systems made up of rigid bodies and flexible Timoshenko beams. The algorithm is then encoded in Mathematica as the package MultiFlex.m and the straightforward application of MultiFlex to two examples with 1 degree of freedom and 14 degrees of freedom, respectively, is presented. The MultiFlex package represents one part of a suite of programs which are being developed by the authors in order to provide entirely symbolic analysis of multi-degree of freedom problems in engineering dynamics.
Original languageEnglish
Pages (from-to)85-98
Number of pages14
JournalMathematics and Computers in Simulation
Issue number1-2
Publication statusPublished - 3 Sep 2004



  • multibody code
  • symbolic state space equations of motion
  • lagrangian approach
  • open loop systems
  • Timoshenko beam

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