Rotational dimensions and directions

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Rotational dimensions and directions

Postby anderscolingustafson » Tue Feb 01, 2011 6:07 pm

I know that when an object is spinning horizontally so that the top and bottom and ana and kata sides are stationary than it is said to either be spinning clockwise or counter clockwise. But what about the other rotational directions such as when an object is spinning so that its top and bottom and left and right side are stationary or when its left and right and ana kata sides are stationary and so on? What are the names of these rotational directions and what are the names of all the rotational dimensions. What are the names of all the rotational directions?
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Re: Rotational dimensions and directions

Postby Keiji » Tue Feb 01, 2011 7:47 pm

Actually clockwise and anticlockwise (or counter-clockwise) are entirely dependent on the perspective; you screw a screw in clockwise, but if you're looking from the other side (usually you wouldn't, because there'd be something in the way, but say you're screwing something on the other side of a wall by feeling it) then you screw it anticlockwise.

In other words, there is no such thing as clockwise or anticlockwise if you only have a plane to determine where the rotation is happening: you also need to know the positive directions of the plane, and then you can say that if you look at the plane such that the x-axis points right and the y-axis points up, you know which way a clockwise rotation goes.
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Re: Rotational dimensions and directions

Postby PWrong » Fri Feb 04, 2011 2:56 am

Didn't we have names for an extension of yaw, pitch and roll?
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Re: Rotational dimensions and directions

Postby Prashantkrishnan » Sun Oct 02, 2016 6:32 pm

The notion of clockwise and anti-clockwise becomes meaningless in 4D.
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Re: Rotational dimensions and directions

Postby wendy » Mon Oct 03, 2016 1:00 am

In 4d, you still have parity of rotation. These are the clifford left and clifford right.

You must remember that ampere's law applies in all dimensions.
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Re: Rotational dimensions and directions

Postby Prashantkrishnan » Mon Oct 03, 2016 12:22 pm

wendy wrote:In 4d, you still have parity of rotation. These are the clifford left and clifford right.

You must remember that ampere's law applies in all dimensions.


When the number of dimensions is more than 3, how do we find the net current crossing a closed loop? In 3D we subtract currents in opposite directions, but in 4D, the current can enter the loop at various angles. And what happens to the right hand thumb rule?
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Re: Rotational dimensions and directions

Postby Prashantkrishnan » Mon Oct 03, 2016 2:35 pm

Also, what would be the nature of magnetic field in 4D? Obviously Biot-Savart law as we know in 3D cannot hold. What would be its form in 4D?
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Re: Rotational dimensions and directions

Postby wendy » Tue Oct 04, 2016 7:56 am

The general form of the ampere law in higher dimensions does not suppose current, but 'circulation'.

A ring here is a division-boundary on a solid, such as the outline of a section against one axis. But the division does not have to be coplanar. Such a ring, when spanned by a surface (N-1 space), gives rise to a 'vector area', which is independent of the shape of the surface. This is the general reflex of the rule m = IA (magnetic moment = current * area).

This means that the ring has a parity, in the form of a circulation, (I), which gives a sense of direction to A (ie the normals to A, which are added vectorially, acquire their sense from the perimeter). As with the ordinary partition of the area into a mesh, and each little mesh-cell has the same I and sense, this replicates in every dimension.
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