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Science Forum Index » Mechanics Forum » Aronhold-Kennedy Theorem...
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| Tom Impelluso... |
 Posted: Tue Jul 29, 2008 3:59 pm |
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Hello all!
Could someone point me to a PROOF of the Kennedy-Arnhold
Theorem?
"When considering three links - i, j, k - the three instantaneous
centers - Pij, Pik, Pkj - are co-linear."
I have seen its use...
I can "intuit" it.
But I would like to see a rigorous proof if one exists.
Thanks!
t. |
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| Brian Whatcott... |
| Posted: Thu Jul 31, 2008 10:12 pm |
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On Tue, 29 Jul 2008 13:59:52 -0700, Tom Impelluso
<impellus at (no spam) attila.sdsu.edu> wrote:
Quote: Hello all!
Could someone point me to a PROOF of the Kennedy-Arnhold
Theorem? "When considering three links - i, j, k - the three instantaneous
centers - Pij, Pik, Pkj - are co-linear."
I have seen its use...I can "intuit" it.
But I would like to see a rigorous proof if one exists.
Thanks!
t.
Here's a google book excerpt that gives a reductio proof of A-K
<http://books.google.com/books?id=GbSDz8Sge8kC&pg=PA53&lpg=PA53&dq=aronhold-kennedy+theorem&source=web&ots=GtRAjRji5J&sig=L9yEp6g_eFOx0fvq2SSOyFexgiY&hl=en&sa=X&oi=book_result&resnum=5&ct=result>
The URL is so long I cannot believe it will survive intact. It is
indeed counter-intuitive to suppose that the three instant centers of
velocity orf links which need not even be connected, lie on a
straight line. Its the line normal to the velocity vector that
confers the 'magic' I suppose. But consider three
disks in a plane spinning each on its own center, disposed in a
triangle. THOSE centers occupy a line??
:-)
BrianW |
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