# What equation are these?

1. Sep 18, 2008

### optics.tech

Does anyone know what equations are these (please see attached image)?

Also, does anyone know these complete equations?

Thank you

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2. Sep 18, 2008

### Mech_Engineer

They look like they could be related to rotational dynamics, as terms for angular speed ( $$\omega$$ ) radius ( $$r$$ ) and time ( $$t$$ ) are in them. It's also possible they are related to some form of harmonic oscillation, based on the $$sin(\omega t)$$ terms I see in there.

However they look like they are probably based a specific geometry, as they don't look generalized to me. Where did you see these equations, and what was the context of their presentation?

Last edited: Sep 18, 2008
3. Sep 18, 2008

### minger

The lambda $$\Lambda$$ and what Mech_ said makes me think they rotordynamic oriented as well.

4. Sep 18, 2008

### FredGarvin

The r/L term is usually a slenderness ratio in shaft dynamics. I'll have to look through my rotor dynamics handbook. I agree with Mech in that I bet this is a derivation for a specific condition/geometry. It definitely is taking me back to the days of harmonic functions and Fourier transforms...

5. Sep 18, 2008

### Mapes

I don't disagree with this, but on the far right of the photo it looks like L is the length of a bar connected to a rotating radial link with length r. That would make

$$\sqrt{L^2-r^2\sin^2\omega t}=L\sqrt{1-\left(\frac{r}{L}\sin\omega t\right)^2}$$,

which appears in one of the equations, the y coordinate of the end of the bar.

6. Sep 19, 2008

### optics.tech

How do you know that the equation is dedicated to specific geometry?

If so, what kind of geometry is it? 2 or 3 dimensional?

7. Sep 19, 2008

### FredGarvin

I think you're right on that. I saw the "a" on the circumference of the circle and thought that r may be the radius of the bar with length L. Your slant is more probable. I wonder if it's just a kinematics equation for a linkage, like you mentioned...