Independent Variable Formulations

  • Wojciech Blajer
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 511)


In Chapter 5 the dependent variable formulations for simulation of multibody systems were described. The derivation of equations of motion in terms of dependent states, though conceptually simple and easy to handle, leads to large-dimension governing DAEs, which results in computationally inefficient algorithms, burdened further with the constraint violation problem. An old and legitimate approach to the dynamics formulation is therefore to use a minimal number of independent state variables for a unique representation of motion by means of pure reduced-dimension ODEs. The numerical integration of the ODEs is usually by far more efficient compared to the integration of the governing DAEs, and the numerical solution is released from the problem of constraint violation. On the other hand, the minimal-form ODE formulations require often more modeling effort and skill. Effective and computer-oriented modeling procedures of this type are thus highly desirable.


Multibody System Nonholonomic System Multibody System Dynamic Constraint Reaction Generalize Coordinate Partitioning 
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© CISM, Udine 2009

Authors and Affiliations

  • Wojciech Blajer
    • 1
  1. 1.Institute of Applied Mechanics, Faculty of Mechanical EngineeringTechnical University of RadomRadomPoland

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