Re: Matrix Mass
- From: WaiteDavid137@xxxxxxxxx
- Date: 28 Oct 2005 08:06:04 -0700
The I subscript is for inertia, not for an element. I didn't intend for
the equation to be in element notation. The equation
f = Ma
as I had inteded it means that the ordinary force as a vector is equal
to the Mass as a matrix times the acceleration as a vector. There is
nothing wrong with doing this and I think it was Steve Carlip that I
first heard suggest that it could be done. An addendum was added to the
relativity faq demonstrating that it could be done but he didn't work
out what the Matrix actually looked like in terms of its components.
Someone asked me what the matrix looked like so I wrote it out. The
only difference between what I wrote out and what he suggested could be
done was that he used it to say three component force is 3X3 matrix M
multiplying three component acceleration whereas to be more general I
extended the definitions of ordinary force and coordinate acceleration
to include a fourth element(not four-vectors). So my equation reads
four component ordinary force is 4X4 matrix M mutltiplying four
component acceleration. To visualise the product take the force and
acceleration to be columb vectors. It works out fine. In element
notation his would read
f^i = M^i_J*a^J
where the Matrix M elements are M^i_J
I didn't want to do that because someone will confuse f and a with
four-vector force F and four-vector acceleration A, but in element
notation mine would read
f^mu = M^mu_nu*a^nu
.
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