More convenient mathematical notation for a simple use case

[I_Try_Math]

TL;DR

Just wondering if there is a better notation when it comes to this simple use case.

So in my textbook there's a basic problem where you solve for the final velocities of two hockey pucks, which happen to have different colors which are red and blue, using conservation of momentum. The notation that the textbook uses to express the final velocities of the pucks is $v_{1,f}$ and $v_{2,f}$ which displays fine for Tex code but I find it inconvenient for handwritten math. The notation that I use is $v_{rf}$ and $v_{bf}$ corresponding to the final velocities of the red and blue puck respectively. That notation seems better to my mind because it emphasizes the conceptual difference of the velocities without just subscripting them with a generic number but still kind of clunky and when doing algebra with it, it just doesn't look that all that elegant with the subscripts all cluttered everywhere. Might be a dumb question but is there a more aesthetically pleasing and elegant notation to use in this case?

I thought maybe a dot above like $\dot v_{r}$ with the dot representing that it's an initial velocity might be a little better but it's already used to notate a derivative. If there's no other commonly accepted notation I'd be interested to see if someone could make a creative one and share it here.

 

[DrClaude]

Don't use the dot, as it has a specific meaning, but there are other diacritics you can use, such as $\bar{v}$ or $\tilde{v}$. You can also use another letter for the variable of one of the two pucks, such as $u$ (which can be confused with $v$ when handwriting), or $w$, such that you would use for instance $v_f$ for $v_{1,f}$ and $w_f$ for $v_{2,f}$.

If you are going to deviate from the notation used by a problem, you should clearly state the notation you are using, and you should revert to the original notation when giving the final answer. Your teacher will appreciate that .

 

[I_Try_Math]

Interesting, I think $\tilde{v_{r}}$ is easy on the eyes and convenient to handwrite. Thanks for sharing that.

 

[jedishrfu]

The dot overhead usually signifies a time deriviative. It was first used by Isaac Newton in his Principia.

In Newton's notation two dots overhead signify the second time derivative:

s(t) --> distance with respect to time

$\dot{s}$ = v --> velocity

$\ddot{s}$ = $\dot{v}$ --> acceleration

 

[FactChecker]

TL;DR Summary: Just wondering if there is a better notation when it comes to this simple use case.

So in my textbook there's a basic problem where you solve for the final velocities of two hockey pucks, which happen to have different colors which are red and blue, using conservation of momentum. The notation that the textbook uses to express the final velocities of the pucks is $v_{1,f}$ and $v_{2,f}$ which displays fine for Tex code but I find it inconvenient for handwritten math.

Inconvenient for handwritten math? Why? Commas are not that hard to do.

The notation that I use is $v_{rf}$ and $v_{rb}$ corresponding to the final velocities of the red and blue puck respectively. That notation seems better to my mind because it emphasizes the conceptual difference of the velocities without just subscripting them with a generic number

If there is some real conceptual difference between the two that is indicated by 'r' versus 'b', I could see your point. Otherwise, I would be needlessly wondering what 'r' versus 'b' signifies, when it signifies nothing. Using '1' and '2' is better if they are just two items with the same physical attributes.

 

[I_Try_Math]

Inconvenient for handwritten math? Why? Commas are not that hard to do.

If there is some real conceptual difference between the two that is indicated by 'r' versus 'b', I could see your point. Otherwise, I would be needlessly wondering what 'r' versus 'b' signifies, when it signifies nothing. Using '1' and '2' is better if they are just two items with the same physical attributes.

It's a personal preference. I don't find the commas necessary, and in this case the r and b subscripts make it easier for me to picture what's going in this type of conservation of momentum problem.

 

[Tom.G]

My 2-cents worth:

The 'comma' seperator has come to indicate which individual of a set is being referenced.

Not very different from indicating which dimension of a multi-dimensioned array is being referred to, as in A _4,3,x or A(4,3,x). Without the commas, you could not know if the A was the name of a single variable or an array with one, two, or three dimensions.

It seems most logical to keep the disambiguation uniform.

Cheers,
Tom