- #1
Kulkid
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Homework Statement
Find the Cartesian coordinates (x, y, z) of a fixed reference frame expressed in terms of the coordinates (x', y' , z) of a rotating frame, which rotates with the horizontal rod HR. Choose the x' -axis to point along the horizontal rod in the direction OA.
Use this to find the Cartesian coordinates (x, y, z) of the pendulum expressed in terms of θ and t
2. Homework Equations
The Attempt at a Solution
I tried this:
##x = x' cos(\omega t)##
##y = y' cos(\omega t)##
##z = z##
##x' = a\hat{i}##
##y' = b sin(\theta)\hat{j}##
##z = -b cos(\theta)\hat{k}##
So: ##\vec{r} = (acos(\omega t), bsin(\theta)cos(\omega t), -bcos(\theta)) ##
Im later supposed to get a Lagrangian that looks like this:
##L =1/2mb^2\dot{\theta^2}+mab\omega cos(\theta)\dot{\theta}+1/2mb^2 \omega^2sin^2(\theta)+mgbcos(\theta)##
but its not quite working. Any tips?