"rot"

Can anyone explain what the mathematical operation of "rot" is. I encountered it whilst reading a book. It just has "rot w" where w is a vector. It appears to be distinguished from curl and the dot product operations.

Reply 1

16characterlimit

From 4 minutes of Googling.

"Curl (mathematics)

blah

The alternative terminology rotor or rotational and alternative notations rot F and ∇ × F are often used (the former especially in many European countries, the latter, using the del operator and the cross product, is more used in other countries) for curl and curl F."

So its probably the same, bear in mind I'm an A Level plebian, so I wouldn't know, Wikipedia does though!

Reply 2

Kevin De Bruyne

I'll just add that it's really annoying when you come across notation that hasn't been defined earlier on or is assumed to be known. :s-smilie:

Reply 3

0le

Original post by 16characterlimit

In one line of text, he uses the cross product, the dot product and rot. Hence I mentioned already that it is distinguished from those two. There does not appear to be any reason for him to use two different notations for the same operation.

(edited 7 years ago)

pic.png5.2KB

Reply 4

16characterlimit

Original post by djpailo

You'll need to consult someone with a higher level of knowledge than me then, though according to Wikipedia rot=curl, so it still works using cross dot and "rot" as distinct operations.

Reply 5

0le

Original post by 16characterlimit

You'll need to consult someone with a higher level of knowledge than me then, though according to Wikipedia rot=curl, so it still works using cross dot and "rot" as distinct operations.

The del operator cross product to a vector is the curl whereas the cross product of two vectors is just a mathematical operation to obtain a third vector which is perpendicular to the other two. Performing both operations mechanically (i.e. doing it on paper) is the same. However, physically, there are some differences. The curl can produce an output vector which is at any angle to the input vector whereas the cross product of two vectors always produces a third vector at right angles to the latter two. This is because the del operator is an operator, whereas the cross product, as far as I looked into it, is only defined rigorously for vectors, and as someone on maths exchange put it, "it just so happens that the operator behaves similarly to a vector for the cross product to work". See Davidson's notes on page 2:

http://www3.eng.cam.ac.uk/DesignOffice/cmiCD02_student/lecturenotes/2001/1b/paper7/vec/notesC/1B2001P7VECL10F.pdf

At first I thought he could just be using "rot" as a placeholder for the del operator symbol, but he also uses the del operator for some other things too..

So in my mind, "rot" must have a specific meaning. I agree the mechanical operation is the same, it will produce a vector, but surely by using rot he is implying something about this vector which is what I'd like to know. I'll have to make an account on maths exchange and ask at some point. I'll post the answer here if I find out.

(edited 7 years ago)

Reply 6

0le

Original post by SeanFM

I'll just add that it's really annoying when you come across notation that hasn't been defined earlier on or is assumed to be known. :s-smilie:

Funnily enough, the book is entitled "informal introduction to blah blah...". When I read a bit of the intro I thought it would just be a causal read which would allow me to gain some physical insight without getting bogged down in mathematics. Yet here I am...