- #1

dyn

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- 61

I have been doing a question on Lagrangian mechanics. I have the solution as well but i have a problem with the way the question is asked regarding dimensions.

The 1st part of the question says that a particle of mass m with Cartesian coordinates x , y , z moves under the influence of gravity on the surface

z = (1/2) In(x

^{2}+y

^{2})

Now this doesn't seem right because the argument of a log should be dimensionless. Also the log of a number is a dimensionless number so the LHS of the equation has dimensions of length wile the RHS is dimensionless.

Following on from this comes my next confusion ; the Lagrangian which is given in polar coordinates involves a term containing (m/2) multiplied by (r dot )

^{2}multiplied by ( 1 + r

^{-2}). This is adding 2 terms together with different dimension which is not allowed

Am i right that the question is written incorrectly or have i got something wrong ?

Thanks