Tangent to several circles

[Guest]

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

[Guest]

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

[Guest]

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

[Math Tutor]

Mr. Lishkov answered:
See the attachment below, please:

[Guest]

center point, X=1113.5235 Y=-3377.8355 Z= 0.0000
radius 3633.0537

[Guest]

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

[Guest]

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

[Math Tutor]

Here is the result from Mr. Lishkov
A system of 3 equations in 3 variables.

[Guest]

must be solved first system of three equations
The second is not true

[Math Tutor]

The file is updated by Mr. Lishkov

[Guest]

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