Rene Ferdinands
10-05-1998, 11:32 AM
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.


Rene' Ferdinands
Department of Physics
University of Waikato
New Zealand

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