Change position on balance system from p to q?

[Richard Murray]

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,

[Richard Murray]

(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:

• In the spring-mass system we use $q$ (but it really is the generalized coordinate).
• In the VTOL examples, we use $x$ and $y$ for the position (overlapping with state and output variables), but we then use $z$ for the state variable.
• In the steering examples, we use $x$ and $y$ for the position, but then we just look at lateral deviation and angle for the controller => $x = (y, \theta)$.
• In the AFM examples (also a type of spring mass system) we use $z_1$ and $z_2$ for the vertical displacement.

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)?

[Richard Murray]

24 Jul: change to $q$

[Richard Murray]

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 $p$.