## Visualization of birotation

### Visualization of birotation

Recently I found this representation of so-called "Tusi-couple" - a mathematical device proposed by 13th century Persian astronomer Nasir al-Din Tusi:

http://upload.wikimedia.org/wikipedia/c ... couple.gif

Here we have two rotational motions - the second having its center upon the periphery of the first one's circle, then a point from the periphery of the second circle performs a simple harmonic motion upon the diameter of a twice bigger circle containing them both.

Can this be seen as model of birotation too?

http://upload.wikimedia.org/wikipedia/c ... couple.gif

Here we have two rotational motions - the second having its center upon the periphery of the first one's circle, then a point from the periphery of the second circle performs a simple harmonic motion upon the diameter of a twice bigger circle containing them both.

Can this be seen as model of birotation too?

### Perhaps rotational vibration

That appears to be only a singular rotation. I would not qualify it as a birotation because the dimensions are not reduced to a waveform--you still have an area, with a point on a curcumference tracing a waveform. With Nehru's counter-rotations, the area collapses to a wave, via the Euler relations.

Though it may be a good analog of the concept of "rotational vibration."

Though it may be a good analog of the concept of "rotational vibration."

Every dogma has its day...

### Here is a great place to

Here is a great place to start for visualizing rotation as it relates to waveforms or space/time oscillations:

http://www.math.utah.edu/~palais/cossin.html

http://www.math.utah.edu/~palais/cossin.html

### Maybe...

Maybe I am wrong, but this "Tusi couple" still seems as birotation to me: there are two rotations - the first one is counter-clockwise around the center, while the second one is clock-wise with a center upon the moving point of the first one. The radii and velocities are equal, only the angles differ with 180 degrees which will change the sign of the cosine in the equation of the second rotation. Thus in this case when we add the two rotations to find the equation of the composite motion the imaginary components will survive and sum up. Thus we again have a simple harmonic motion with an amplitude twice bigger than that of the rotations, only here it is along the imaginary, (i.e. vertical) axis, while the horizontal (i.e. real) motions neutralize each other. But after all isn't it just a convention that we have choosen to consider the vertical axis as imaginary?

Still, in this representation the centers of the two opposite rotations don't coincide - I guess that's the main difference from the birotation. I am not sure if it's possible to rotate this way across the unit border, but I still have difficulties with grasping the concept in general. (Even the original Larson's notion about the rotation of a photon seems quite vague to me and he usually looses me when begins to explain his atomic model).

Still, in this representation the centers of the two opposite rotations don't coincide - I guess that's the main difference from the birotation. I am not sure if it's possible to rotate this way across the unit border, but I still have difficulties with grasping the concept in general. (Even the original Larson's notion about the rotation of a photon seems quite vague to me and he usually looses me when begins to explain his atomic model).

### Radius Vector rotation

Yes, you are correct. They did not draw the second rotation in the animation and I overlooked it (was in a bit of a rush that day). This is actually very similar to one of Nehru's old diagrams on birotation:

Where you have one rotation with its center on the circumference of another. (Neither rotation is drawn here; just the rotations of a radius vector.)

The difference between this model and the rotations on a common axis, is that the common axis rotation has two, opposite directions of the SAME aspect--either space OR time--and therefore they are in phase (axial). When you have a birotation that has one component in space and the other in time, there is a 90-degree phase difference between the perceived rotational centers, so you end up with each center intersecting the circumference of the other. (This is the case in molecular bonding, where positive/temporal rotation matches negative/spatial rotation.)

Where you have one rotation with its center on the circumference of another. (Neither rotation is drawn here; just the rotations of a radius vector.)

The difference between this model and the rotations on a common axis, is that the common axis rotation has two, opposite directions of the SAME aspect--either space OR time--and therefore they are in phase (axial). When you have a birotation that has one component in space and the other in time, there is a 90-degree phase difference between the perceived rotational centers, so you end up with each center intersecting the circumference of the other. (This is the case in molecular bonding, where positive/temporal rotation matches negative/spatial rotation.)

Every dogma has its day...

### Bruce

Bruce

"Where you have one rotation with its center on the circumference of another. (Neither rotation is drawn here; just the rotations of a radius vector.)

is this like the Earth rotating on the circumference of circle made by the rotating Sun?

i'm desparately look for "pictures"

"Where you have one rotation with its center on the circumference of another. (Neither rotation is drawn here; just the rotations of a radius vector.)

is this like the Earth rotating on the circumference of circle made by the rotating Sun?

i'm desparately look for "pictures"

### Coplanar rotation

Yes. The difference being would be that you would need the same angular velocity (rotational speeds), and in opposite directions to reduce to a sine wave. I may have done an animation on this somewhere; I'll look around.is this like the Earth rotating on the circumference of circle made by the rotating Sun?

Every dogma has its day...

### Re: Visualization of birotation

Here is a visualization I did of Nehru's concept of birotation, as an animated GIF, expressing the Euler equation:

- The disk radius is 1 natural unit.
- The separation between disk centers is 1 unit.
- The rotations have the same starting phase.
- The angular velocities are equal and opposite.
- The magnitude of the resulting cosine wave is 4 units.

Every dogma has its day...

### Re: Visualization of birotation

That's a very helpful visualization.bperet wrote:Here is a visualization I did of Nehru's concept of birotation, as an animated GIF, expressing the Euler equation:

birotation.gifSince we measure things by diameter, not radius, the resulting wave has a magnitude of twice the diameter of the disks. This is where the "2" on the cosine term comes in.

- The disk radius is 1 natural unit.
- The separation between disk centers is 1 unit.
- The rotations have the same starting phase.
- The angular velocities are equal and opposite.
- The magnitude of the resulting cosine wave is 4 units.

I am confused though, by the 1 unit separation. I thought the definition of motion was the ratio of s/t expressed in 3 dimensions at a single conceptual location. This biroration is of two locations, which should make it an aggregate rather than a single motion.

What piece am I missing?

### Re: Visualization of birotation

SoverT wrote:I thought the definition of motion was the ratio of s/t expressed in 3 dimensions at a single conceptual location. ...

What piece am I missing?

If you read

**this**Bruce's post, you will find out that he is writing about three s/t ratios.

bperet wrote:The confusion with dimensionality in the RS stems from applying the rules of the conventional frame of reference (space only, with width, height and depth) to a universe based on the ratio of motion--three dimensions of speed, (s/t, s/t, s/t).