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  • 2D LAGRANGIAN MODELLING - RIGID BODIES

    Hello! I am a biomechanical engineer at the University of Waikato, and I am
    carrying out research in the area of sports biomechanics - particularly of
    the cricket bowling action. I have been successful in generating the
    Lagrangian equations of motion for any number of segments of a multi-body
    system. This means that I am able to generate inverse solutions for any
    trajectory of the system (Note: 2D analysis only).

    However, I am chiefly interested in generating forward solutions. For two
    segment systems this is no problem. However, for three segments and above I
    find that symbolic software systems such as Maple V are unable to cope with
    the length and complexity of the equations, even in the process of
    converting 2nd order DE's into a system of 1st order DE's, i.e. by just
    using the Solve command. I am finding that Mathematica has similar problems
    in manipulating equations of five segments and above. Has anyone got any
    experience in numerically solving Lagrangian equations for multi-body
    systems, so as to provide a forward solution treatment of the problem? What
    are some good numerical approaches? Can the dynamics of the system be
    manipulated so that the equations can be simplified? Are there approaches
    that would simplify the equations generated - e.g reduce the number of
    variables to be computed at any one time? Is there a way of using lists
    which are progressively updated after each round of numerical analysis?
    etc. I have some lovely complex equations, but can't do much with them!

    Your responses would be most appreciated.

    Regards

    Rene' Ferdinands
    Department of Physics
    University of Waikato
    New Zealand
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