Change position on balance system from p to q?
On 29 May 2019, Karl wrote: I was reading parts of the book yesterday. In the cart-pendulum problem we are using $p$ to denote the positon of the cart, see for exampel Fig 3.6. I think $p$ is not a good notation, it is better to use $q$ which is a standard notation for generalized coordinates, $p$ is often used to denote momentum $p=m\dot q$. I realize that we have to do a several changes but I think it is worth it,
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reporter 24 Jul: change to $q$
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Fixed in commit fa7e9a5. Defined a new macro in macros.tex called \balpos and used this in place of $p$ throughout. Currently \balpos is set to $q$. There is also a note on first use to avoid confusing with the full configuration.
Also: $p$ was a bad choice because we later talk about the poles, also called $p$.
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(from 30 May 2019 e-mail)
I agree that $p$ can conflict with momentum. One issue is that $q$ is not the full set of generalized coordinates for the balance system => if we go that route we might want to use $q_1, q_2$ instead of $p, \theta$?
Alternatively, we could use some other symbol besides $p$ (generalized momenttum) or $x$ (system state). Some other choices we made:
So things are a bit all over the map. Do we want to fix any of these, or just change $p$ to $q$ in the balance system (consistent with spring-mass notation, but not quite representing the full generalized coordinates)?