cancel
Showing results for 
Search instead for 
Did you mean: 
cancel
Showing results for 
Search instead for 
Did you mean: 

Center of gravity and center of ???

SOLVED
ValeryOchkov
Ruby I

Center of gravity and center of ???

I try to calculate the center of gravity one not simple plane figure.

What is it the red point?

2-Centers.png

See more please

Center of mass

1 ACCEPTED SOLUTION

Accepted Solutions

Re: Center of gravity and center of ???

45 REPLIES 45

Re: Center of gravity and center of ???

3D variant

3D-Center-Mass.png

Re: Center of gravity and center of ???

Where did you learn that the center of gravity was y = 0.5?

Re: Center of gravity and center of ???

y:=0.5m was just his guess value for the subsequent Minimize function.

We are all in agreement that the center of mass is at y=61cm.

What is the red point?  As defined by the equation, it is the point with the shortest distance to the mass.  If it has a name, I don't know it.

Re: Center of gravity and center of ???

Okay, sorry, didn't read carefully.

But when I do the same thing:

So I don't see where 74.883 came from.

Re: Center of gravity and center of ???

Fred,

Your summation should go from i = 0 to n1 (not n1-1); however, this will make a negligible difference.  You would want n1-1 if you had defined n1 with the rows() function, but you used last(), so the -1 is not needed.

The difference in the calculations is that Valery took the square root before summing.  When I do the same in your worksheet, I get the same 74.883 that Valery got.

Re: Center of gravity and center of ???

So do I!

Why is it wrong?  Minimizing X^2 and minimizing X should give the same result, shouldn't it?

Re: Center of gravity and center of ???

That's what I thought at first, but we're not minimizing X or X^2.  We're minimizing a sum.

Here's a quick graph:

Capture.PNG

The points near y=0 are furthest from x=0, so their effect is stronger on S1 than they are on S2.

Re: Center of gravity and center of ???

I think you're right!

I took histograms of X and Y:

More of the Y's are near the top, while most of the X's are  at he ends.

Note that the mean of Y gives the same answer as S2 (aka Sq):

 

Re: Center of gravity and center of ???

Here's a simplified version of the problem worth pondering:

Capture.PNG

Re: Center of gravity and center of ???

Mark Gase написал(а):

Here's a simplified version of the problem worth pondering:

Capture.PNG

One more example

CG-Triangle.png

Re: Center of gravity and center of ???

I find it ever so sad to see that you generate a lot of data, then throw away the largest part of it.

How about:

So that you keep your n points.

Luc

Re: Center of gravity and center of ???

LucMeekes написал(а):

I find it ever so sad to see that you generate a lot of data, then throw away the largest part of it.

How about:

So that you keep your n points.

Luc

Sorry, but better to have same density of points in horizontal and vertical dimensions!

Not 0..1 and 0..1/2, but 0..1 and 0..1

And second - Do you red my letter about your address?

Re: Center of gravity and center of ???

Does this help?

If you change the 'thickness' of the semi-circle, the amount of points with y above y1 doesn't change as much as y1.

Extreme example:

Luc

Re: Center of gravity and center of ???

Luc,

The way you have defined the data points, there are more near the inside radius than the outside radius.  This is especially visible in your last graph.

Valery's setup made the points uniformly distributed throughout the whole area.

This will skew some of your calculations.

Re: Center of gravity and center of ???

Mark,

I agree.

Luc

Re: Center of gravity and center of ???

Mark Gase написал(а):

Luc,

The way you have defined the data points, there are more near the inside radius than the outside radius.

It is not correct but more nice!

Re: Center of gravity and center of ???

Better like this?

Luc

Re: Center of gravity and center of ???

Luc, to get a uniform distribution of points over a circular area you need to generate a uniform distribution for r^2 and then take the square root to get r (as well as generating a uniform distribution for phi, of course).

Alan

Re: Center of gravity and center of ???

Ah, sure Alan! Why didn't I think of that. So like this:

Luc

Re: Center of gravity and center of ???

Re: Center of gravity and center of ???

Mark Gase написал(а):

The red point is the geometric median.

We must check in on one triangle with three medians!

Re: Center of gravity and center of ???

I think the geometric median and the center of gravity must be one point .

Why?

See please two method of the searching this point:

1-Wiki.png

hand.png

But we have by using our (Monte-Carlo) method;

Points-Blue-Red.png

Re: Center of gravity and center of ???

Sorry!

This point is

Barycenter - Wikipedia

or geometric center.

If our figures have constant density - geometric center = mass center!

Why we have: geometric center and mass center are two different points at constant density?

Re: Center of gravity and center of ???

From Barycenter - Wikipedia:

In geometry, the term "barycenter" is synonymous with centroid, the geometric center of a two-dimensional shape.

That means:

barycenter = centroid = geometric center = center of mass w/ constant density

Valery Ochkov wrote:

Why we have: geometric center and mass center are two different points at constant density?

You have two points because the geometric median is not the same as the geometric center.

Re: Center of gravity and center of ???

Mark Gase написал(а):

From Barycenter - Wikipedia:

In geometry, the term "barycenter" is synonymous with centroid, the geometric center of a two-dimensional shape.

That means:

barycenter = centroid = geometric center = center of mass w/ constant density

Valery Ochkov wrote:

Why we have: geometric center and mass center are two different points at constant density?

You have two points because the geometric median is not the same as the geometric center.

Sorry, Mark,

but with constant density the geometric median is the same as the geometric center. Or?

Re: Center of gravity and center of ???

Yes, Mark!

It is the geometric median!

But what is the name this point in German, French, Italian, Russian....

Wiki.png

Re: Center of gravity and center of ???

Center of Gravity... 4D-body

4D-Center-Mass.png

Re: Center of gravity and center of ???

Two pictures and sheets for thinking!

Three points! Why?

3-points.png

One point!

1-Center.png

Re: Center of gravity and center of ???

Center of Gravity... 4D-body

Where is the plot?  I want an animated XYZ plot with W as time.

Announcements