The graphic of |F||D|=1 is hyperbola or ellipse

AI Thread Summary
The discussion centers on the law of the lever in equilibrium, expressed as |F||D|=1, where F represents force and D represents distance from the lever's center. It explores the implications of different mathematical representations, such as |F|=|x-y| leading to a hyperbola and |F|=x-iy resulting in an ellipse or imaginary hyperbola, indicating repulsive and attractive interactions, respectively. The common version of the law includes contributions from the rest of the system, denoted as |F_r| and |D_r|. The author invites further exploration of these concepts on their website, specifically in the "Dynamics of the lever" section. Understanding these relationships is crucial for grasping the underlying mechanics of levers.
dedaNoe
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|F||D|=1 is the simplest form of the law of lever in equilibrium.
If |F|=|x-y| and |D|=x+y then |x^2-y^2|=1 is an real hyperbola.
In this case the interaction is repulsive.
If |F|=x-iy and |D|=x+iy then x^2+y^2=1 is an real ellipse or imaginary hyperbola.
In this case the interaction is attractive.

www.geocities.com/dedaNoe
www.geocities.com/dedaNoe/lever.pdf
 
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Perhaps it would help us understand what in the world you are talking about if you told us what F and D mean!
 
Yeah sure!

F is the force acting in D distance from the center of the lever.
The common version of the law of lever is:
|F||D|=|F_r||D_r|=1
here |F_r| is the sum of the forces from the rest of the system and
|D_r| is the sum of the distances from the rest of the system.

I have more on this on my page:
www.geocities.com/dedaNoe
section "Dynamics of the lever".
 
I think we've seen enough.
 

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