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

In summary, the conversation discusses the law of lever in equilibrium and its simplest form, |F||D|=1. It also talks about the interaction being repulsive or attractive, depending on the values of F and D. The websites www.geocities.com/dedaNoe and www.geocities.com/dedaNoe/lever.pdf are mentioned as sources for further information on the topic. The conversation also mentions the common version of the law of lever and provides a link to more information on the dynamics of the lever.
  • #1
dedaNoe
52
0
|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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  • #2
Perhaps it would help us understand what in the world you are talking about if you told us what F and D mean!
 
  • #3
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".
 
  • #4
I think we've seen enough.
 

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

1. Is the graphic of |F||D|=1 a hyperbola or an ellipse?

The graphic of |F||D|=1 can be either a hyperbola or an ellipse, depending on the values of |F| and |D|.

2. How can you determine whether the graphic is a hyperbola or an ellipse?

You can determine whether the graphic is a hyperbola or an ellipse by calculating the eccentricity of the curve. If the eccentricity is greater than 1, the graphic is a hyperbola. If the eccentricity is less than or equal to 1, the graphic is an ellipse.

3. What is the definition of eccentricity?

Eccentricity is a measure of how much a conic section deviates from being circular. It is calculated as the ratio of the distance between the foci (|F|) to the length of the major axis (|D|).

4. Can the graphic of |F||D|=1 be a circle?

No, the graphic of |F||D|=1 cannot be a circle. A circle has an eccentricity of 0, which means that the distance between the foci and the length of the major axis are equal. In the equation |F||D|=1, the distance between the foci and the length of the major axis are always different, so the eccentricity is always greater than 0.

5. Are there any real-life applications of this equation?

Yes, this equation has many real-life applications in fields such as physics, engineering, and astronomy. It is commonly used to represent the orbits of celestial bodies and the trajectories of objects in motion. It can also be used to model the behavior of electric and magnetic fields.

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