Tangent to several circles

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Tangent to several circles

Postby Guest » Tue Dec 06, 2011 3:24 pm

Dear Math Teacher;
I work in Rock Mechanics and we have a standard methodology of description of State of Stress called Mohr Circle... It is basically a series of circles with their centers lying on the X axis and having various radius. A rock Mechanics Parameter called MOHR ENVELOP is a curve (most probably a Hyperbola) that is tangent to all those circles... 'm trying to find th equations of such a Hyperbola that would TANGENT to such several circles... any clue? (I was able to extract and apply (on Mathematica) the equation of a line that is tangent to two circles)

Thank you

Yasser
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Re: Tangent to several circles

Postby Guest » Tue Dec 06, 2011 4:34 pm

Hello,

When should you be ready?
At this point, I work on other very urgent orders.
Please, send me more details.
I will try to help.

e-mail: wml@abv.bg

V. Lishkov
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Re: Tangent to several circles

Postby Guest » Wed Dec 07, 2011 2:15 am

Thank you...
Pls find below the description of the problem in mathematical format:
Suppose that I have three circles:
Circle 1: {95,0}, radius: 105
Circle2: {350,0}, radius: 170
Circle3: {700,0}, radius: 230

in Rock Mechanics, those circles represent states of stresses at various points and various conditions, and we know that the ENVELOP to those circles constitute what we call Mohr Envelop (a Curve that is most probable a Hyperbola, and that is Tangent to ALL circles)

So the problem is: how to find mathematically the equation of that Envelop (hyperbola that is tangent to all three circles)...

Thank you in advance

Yasser
Guest
 

Re: Tangent to several circles

Postby Math Tutor » Wed Dec 07, 2011 5:39 am

Mr. Lishkov answered:
See the attachment below, please:
Attachments
Untitled.png
Untitled.png (13.05 KiB) Viewed 1482 times

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Re: Tangent to several circles

Postby Guest » Wed Dec 07, 2011 5:59 am

center point, X=1113.5235 Y=-3377.8355 Z= 0.0000
radius 3633.0537
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Re: Tangent to several circles

Postby Guest » Wed Dec 07, 2011 6:14 am

This is EXACTELY what I want, but I want it as a Mathematical Formula (I use Mathematica 8.1 to generate the circles out of a state of stress and would like to generate also the Hyperbola out of a mathematical formula, so I may use it for further processing: Differentiation, integration, state of stress comparisons, etc.)...
Thank you in Advance

Yasser
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Re: Tangent to several circles

Postby Guest » Wed Dec 07, 2011 7:33 am

well
I'll see to bring out some form or system
maybe tomorrow
Guest
 

Re: Tangent to several circles

Postby Math Tutor » Wed Dec 07, 2011 6:37 pm

Here is the result from Mr. Lishkov
A system of 3 equations in 3 variables.
Attachments
Points.docx
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Re: Tangent to several circles

Postby Guest » Wed Dec 07, 2011 7:12 pm

must be solved first system of three equations
The second is not true
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Re: Tangent to several circles

Postby Math Tutor » Thu Dec 08, 2011 2:51 am

The file is updated by Mr. Lishkov
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Points.docx
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