Notation for generalized coordinates

[Isaac0427]

I have seen both r_k and q_j both used to represent generalized coordinates in the Lagrange equations. Are these both the same things? Does it matter which you use?
Thanks!

 

[Orodruin]

No, what you are calling things are typically completely conventional. You could call energy R, mass x, and the speed of light T and you would have R = xT^2 - nobody would understand you if you did not specify what notation you were using though. The notation I have seen the most is to use q for generalized coordinates, but it really does not matter as long as you specify what you are doing and use a notation which is not inherently confusing.

 

[Isaac0427]

No, what you are calling things are typically completely conventional. You could call energy R, mass x, and the speed of light T and you would have R = xT^2 - nobody would understand you if you did not specify what notation you were using though. The notation I have seen the most is to use q for generalized coordinates, but it really does not matter as long as you specify what you are doing and use a notation which is not inherently confusing.

Ok, but Wikipedia used both in the same article (even in the same equation). Are these just differing authors or is r_k different?

 

[nasu]

If you mean this page
https://en.wikipedia.org/wiki/Lagrangian_mechanics

they don't use "r" for generalized coordinates but for the position vectors.

 

[Isaac0427]

If you mean this page
https://en.wikipedia.org/wiki/Lagrangian_mechanics

they don't use "r" for generalized coordinates but for the position vectors.

But they use them in replace of q_j in the Lagrange equations of the first kind.

 

[nasu]

The components of the position vectors form a possible set of "generalized" coordinates.
So you can write the equations in terms of them.
Have you read the article? The part when they say that you can go to a more general case, by defining generalized coordinates, q?