Writing the Lagrangians for different frames depending on how "the ball is dropped"

[gionole]

I wanna be checking homogeneity of space(only interested in vertical) for simplicity and example we can do is "ball is dropped". To check homogeneity, we use either passive or active transformation and I'm interested in lagrangians.

I heard that we can write lagrangians such as: $L = \frac{1}{2}m\dot q^2 - mgy$ and $L' = \frac{1}{2} m\dot q'^2 - mg(y'+a)$. This comes from the fact that $y = y'+a$. (we seem to have y and y' frame).

Question 1: it seems to me that lagrangians that I wrote are an example of passive transformation, because of $y = y'+a$. It's like the ball is only dropped from single location(one experiment), but we write lagrangians for the ball such as seen from each frame. Is this right ? as in, am I right that this is passive, or can we also call it active ?

Question 2: Active transformation seems such as ball must be dropped from 2 different locations(2 different locations). So we drop a ball from some height, and then we move up and drop it from higher location. How would we go about writing Lagrangians for each experiment ? using the same lagrangians as shown above doesn't seem correct to me, as I think it's passive.

 

[berkeman]

Don't you already have a thread on this?

https://www.physicsforums.com/threa...determining-experiments.1055989/#post-6936694

 

[gionole]

@berkeman would love to remove that thread as the question there is not asked correctly. but i can't delete it.

 

[berkeman]

@berkeman would love to remove that thread as the question there is not asked correctly. but i can't delete it.

Okay, I closed off the previous thread with a note pointing to this improved version here.

 

[gionole]

@berkeman can you close this as well ? Don't want people to spend time on it. I've figured it out. Thanks.

 

[berkeman]

Sure, thanks for the heads-up. I've closed off this thread now; I'm glad that you figured it out.