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Center of gravity and center of ???

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Re: Center of gravity and center of ???

Mark Gase написал(а):

Center of Gravity... 4D-body

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

I will do it.

But at first we must solve problems of the 3D body with its centers.

Re: Center of gravity and center of ???

Mark Gase написал(а):

Center of Gravity... 4D-body

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

Mark! Give me please the f(x, y, z, w) function and see

Mathcad and Tomography

PS

Mark!

Have you read my letter to You?

Re: Center of gravity and center of ???

Mark and all!

Is this correct center of gravity 3D body?

Fig-5-3D-Center-Mass.png

Re: Center of gravity and center of ???

Yes, those are the coordinates of your CG.  But why are you working so hard?  The simple mean gives you more accurate answers:

Re: Center of gravity and center of ???

Fred Kohlhepp написал(а):

Yes, those are the coordinates of your CG.  But why are you working so hard?  The simple mean gives you more accurate answers:

Why so hard? We can calculate CG of plate with not constant density - one part is wood, the second - iron!

Re: Center of gravity and center of ???

If you have two materials with different densities you do a  weighted average:

Re: Center of gravity and center of ???

Re: Center of gravity and center of ???

Maybe all (or none) of them.

I suppose calculating the population would give the demographic midpoint, so that is ruled out here. Just geographical data.

Do you include mass of mountains (+ ) and valleys (- )?

What about water mass of lakes and rivers?

OK, maybe it's just about the 'surface':

Do you include sloped surface of mountains and valleys?

What about sea level (some parts of land are flooded daily)?

Luc

Re: Center of gravity and center of ???

I have seen two of them - in Ukraine and Lithuania.

It will be good to see on those marks the calculations (in Mathcad)!  

Re: Center of gravity and center of ???

Fred Kohlhepp написал(а):

If you have two materials with different densities you do a  weighted average:

We must have same density of points! But points can have different weight!

Re: Center of gravity and center of ???

Need to think.

Re: Center of gravity and center of ???

The extension to two materials is straightforward - see 2D example below.  The further extension to 3D is also straightforward (as long as you remember to replace R^2 by R^3, and take cube roots instead of square roots, etc.);

semi_a.PNG

semi_b.PNG

Alan

Re: Center of gravity and center of ???

AlanStevens написал(а):

The extension to two materials is straightforward - see 2D example below.  The further extension to 3D is also straightforward (as long as you remember to replace R^2 by R^3, and take cube roots instead of square roots, etc.);

Alan

Yes! It is a piece of watermelon with one grain in the center of gravity

WM.png

This picture will be on my collection of art objects with Math sense.

See please http://twt.mpei.ac.ru/ochkov/TTMI/21/21.01all.png

Re: Center of gravity and center of ???

5 grains of the piece of watermelon! Do yo know more?

WM-N.png

Re: Center of gravity and center of ???

One more example

Fig-6-Random-Figure.png

Re: Center of gravity and center of ???

Our method of searching the center of gravity (mass) has a name Pointillism - Wikipedia

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