# Rotation around a tilted axis.

• cake21
In summary,The author suggests using a formula to rotate an object about a tilted axis. They mention a method of using quaternions and converting them to a linear transformation.
cake21
I am writing a little code that should make an object revolve around a tilted axis.

Here is what I have:
-The center coordonates
-A normal array (3 numbers between 0 and 1);
-position of the object.

Is there a way to do this?

I think:
http://en.wikipedia.org/wiki/Rodrigues'_rotation_formula
Should be it , but I can't work out how to use it. Does the formula return an array?

I can't work out how to use it. Does the formula return an array?
Which formula in that article are you talking about?

If you want a conceptually simple way of doing it, consider this:

Do you know how to write code that would change from one coordinate system to another? If you change coordinates so that the "center" of the rotation becomes the origin in the new coordinate system and the axis of rotation becomes the z-axis in the new coordinates system then you can apply the formula for rotating an object about the z-axis. Get the coordinates of interest in the new coordinate system and then transfer those coordinates back to the original coordinate system.

I've read articles by people who do computer animation that say that using quaterions is the best way to deal with the motion of objects. Are you doing animation?

cake21 said:
I am writing a little code that should make an object revolve around a tilted axis.

Here is what I have:
-The center coordonates
-A normal array (3 numbers between 0 and 1);
-position of the object.

Is there a way to do this?

I think:
http://en.wikipedia.org/wiki/Rodrigues'_rotation_formula
Should be it , but I can't work out how to use it. Does the formula return an array?

Hey cake21 and welcome to the forums.

One method you might want to consider is to use quaternions and then after you computer the final output quaternion, convert it to a linear transformation (matrix) and then apply that matrix to the points you need to do.

The reason why I recommend this is because if you want to multiple rotations, or some something like rotation interpolations, quaternions are probably the best way of doing this, and building a quaternion library is not a hard thing to do either.

## 1. What is rotation around a tilted axis?

Rotation around a tilted axis refers to the movement of an object or body around an axis that is not perpendicular to the plane of its rotation. This means that the axis is tilted at an angle, causing the object to move in a circular path that is not parallel to the ground.

## 2. What causes rotation around a tilted axis?

Rotation around a tilted axis is caused by an external force acting on the object or body. This force can be gravity, friction, or any other force that is applied at an angle to the axis of rotation.

## 3. How does rotation around a tilted axis affect the object's movement?

The tilt of the axis of rotation affects the object's movement by changing the direction of the rotational force. This results in a curved path of motion instead of a straight one.

## 4. What are some examples of rotation around a tilted axis in real life?

A common example of rotation around a tilted axis is the Earth's rotation around its axis, which is tilted at an angle of approximately 23.5 degrees. This tilt is what causes the changing seasons on our planet. Another example is the rotation of a spinning top, which is tilted at an angle as it spins.

## 5. How does rotation around a tilted axis affect the object's stability?

The tilt of the axis of rotation can affect the object's stability by changing its center of mass. If the center of mass is not aligned with the axis of rotation, the object may become unstable and fall over. This is why objects such as tops and gyroscopes are designed with a low center of mass to maintain stability during rotation around a tilted axis.

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