Dimensional analysis

  • Thread starter princejan7
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  • #1
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Homework Statement


How do I set up a matrix to find the combination of ( M(L^2)/T ) and I ( L^4)
that results in units of M/ ( L^2 T^2 ) ?

Homework Equations




The Attempt at a Solution


I think it looks something like
[ 1 0
2 4
-2 0 ]
*
[ a1, a2, a3]
=
[1 -2 -2]

but the dimensions of those matrices aren't right
 

Answers and Replies

  • #2
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Given:

Y = M * X

Are you trying to get a vector Y with units of measure of M / ( L^2 T^2 ) from a vector X with units of measure M(L^2)/T multiplied with matrix M? or is this a dot product?
 
  • #3
Stephen Tashi
Science Advisor
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Homework Statement


How do I set up a matrix to find the combination of ( M(L^2)/T ) and I ( L^4)
that results in units of M/ ( L^2 T^2 ) ?
That statement of the problem isn't clear. (What would "a combination" mean in this context? ) Try stating the problem as it is actually worded.

I think it looks something like
Matrices can't be reliably displayed using ordinary typing. You can resort to LaTex https://www.physicsforums.com/help/latexhelp/ In the meantime, it might be better to use notation like [1,2,-2]^T to denote a column vector.

To have valid multiplication In your work you'd have to multiply on the left by the row vector:

[itex] \begin{bmatrix}a_1&a_2&a_3 \end{bmatrix} \begin{bmatrix}1&0\\2&4\\-2&0 \end{bmatrix} = \begin{bmatrix} 1\\-2\\-2 \end{bmatrix} [/itex]

but I don't know if that equation is appropriate, because I don't know what problem you are solving.

Are you trying work a problem similar to the examples shown in the Wikipedia article http://en.wikipedia.org/wiki/Buckingham_π_theorem ?
 
  • #4
haruspex
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jedishfru, Steven,

princejan7 is trying to solve ##\left(\frac {ML^2}T \right)^{a_1}\left(L^4\right)^{a_2} = \frac M{L^2T^2}##. This leads to the matrix equation shown...
except there is no a3, the a1, a2 should be a column vector, and either the problem has been stated incorrectly or the -2 at lower left of the matrix should be -1.
## \begin{bmatrix}1&0\\2&4\\-1&0 \end{bmatrix} \begin{bmatrix}a_1&a_2 \end{bmatrix}^T= \begin{bmatrix} 1\\-2\\-2 \end{bmatrix}##
Note: there is no solution. princejan7 , is there perhaps some third input parameter? Or is the -2 right in the matrix (which would permit a solution)?
 

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