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.

Regards

Rene' Ferdinands

Department of Physics

University of Waikato

New Zealand

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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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To unsubscribe send UNSUBSCRIBE BIOMCH-L to LISTSERV@nic.surfnet.nl

For information and archives: http://www.bme.ccf.org/isb/biomch-l

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