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24-Ruby IV

## Center of mass

I would like to define a Center of mass - Wikipedia

At first by help one experiment

and then (after a scanning the figure) by Mathcad help

Do you  know more quickly method?

ACCEPTED SOLUTION

Accepted Solutions

Here is how I would have approached:

Or, programmatically:

Both of these methods calculate almost instantly.

Quickly looking at your calculations, I did not follow what you were doing.  What's wrong with my approach compared to yours?

25 REPLIES 25
24-Ruby IV
(To:ValeryOchkov)

I have got the solution but it needed... 5 hr. Not from me but from my PC

Valery,

I believe you made the following error:

The matrix indices should be i1 and j1.

As a result, you found the center of the picture frame:

350 / 2 = 175

385 / 2 = 192.5

24-Ruby IV
(To:MJG)

Thanks, Mark

Now I am going to bed. I will say tomorrow the resultat

23-Emerald I
(To:ValeryOchkov)

You can integrate the boundary curves.

45 minutes start to finish:

24-Ruby IV
(To:Fred_Kohlhepp)

Thanks, Fred!

But I see one error

25-Diamond I
(To:Fred_Kohlhepp)

Well done! I guess I would have rather used linear interpolation.

But the method would not work for something like the following, right?

We would have to resort to algorithms from computer graphics to determine the boundary, but I am too lazy to dig in an implement it. maybe its less work to digitize the outline by other means and import the result into Mathcad.

Then we could use the formula for polygons rather than using integrals, like so (this for the original graphics using your X, X.l and X.r):

Regards,

Werner

23-Emerald I
(To:Werner_E)

Werner,

You'd have to break a complex shape into several simpler ones (that you could integrate.  Once you have areas and CG's for each finding whole is simple

25-Diamond I
(To:Fred_Kohlhepp)

Yes, but its quite some efforts to do it automatically in an all purpose CG finding routine, I guess.

24-Ruby IV
(To:Werner_E)
 Werner Exinger написал(а): Well done! I guess I would have rather used linear interpolation. But the method would not work for something like the following, right? Better

Using my method (see post below), I calculate the COM for your woman to be (169.545, 388.775).

The image is 336 x 897 pixels.

24-Ruby IV
(To:MJG)

Thanks? bot it is too simple...

I would argue that your method is too complex.

24-Ruby IV
(To:MJG)

Sorry,

we must find a center of mass, not a center of gravity

23-Emerald I
(To:ValeryOchkov)
 Valery Ochkov wrote: Sorry, we must find a center of mass, not a center of gravity

When is it different?

"Center of gravity is the point in a body around which the resultant torque due to gravity forces vanish. That means that for any rigid body, the two points are the same, because you can model rigid bodies in free fall as if gravity acted only on the center of mass, and forces on the center of mass make no torque."

24-Ruby IV
(To:Fred_Kohlhepp)
 Fred Kohlhepp написал(а): Valery Ochkov wrote: Sorry, we must find a center of mass, not a center of gravity When is it different? The different is when we have non parallel gravity field - a big body in space near Earth. I think so.
24-Ruby IV
(To:MJG)
 Mark Gase написал(а): I would argue that your method is too complex.

But I can have this figure

24-Ruby IV
(To:ValeryOchkov)

Or so

24-Ruby IV
(To:MJG)
 Mark Gase написал(а): Using my method (see post below), I calculate the COM for your woman to be (169.545, 388.775).

She (from the famous  movie) has the COM in the other point as by us

Here is how I would have approached:

Or, programmatically:

Both of these methods calculate almost instantly.

Quickly looking at your calculations, I did not follow what you were doing.  What's wrong with my approach compared to yours?

23-Emerald I
(To:MJG)

EXCELLENT!

You've replaced my integration (with it's troublesome edge/function needs) with the simple summations.

Impressive!

24-Ruby IV
(To:MJG)

24-Ruby IV
(To:MJG)

Center of gravity and center of ???

25-Diamond I
(To:ValeryOchkov)

Here is another simpler approach if the area is given by a pixel graphics

EDIT: Oops, sorry. Had not seen that Mark already suggested this approach.

24-Ruby IV
(To:ValeryOchkov)

One check

24-Ruby IV
(To:ValeryOchkov)

You can find CG by using our Monte-Carlo method

(from Kirsanov book http://vuz.exponenta.ru/PDF/tm2.pdf)

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