# Rotation operators on a sphere, around x and y axis

• I
• Emily111
In summary, the conversation is about finding a name for a rotation operator that rotates the sphere around the x and y axes. The speaker, who is a translator, mentions that their text is about rotations around the azimuthal nodal lines on the sphere. They ask if there is such a thing as a "nodal rotation operator" and later confirm that the author of their text has invented the term. The speaker believes that "nodal rotation operator" is a suitable name for this type of rotation operator.
Emily111
I need to start by saying that I'm not a physicist, nor a student of physics. I'm a translator, and my text is about rotations around the azimuthal nodal lines on the sphere.

I need to find a name for a particular type of a rotation operator, which rotates the sphere around the x and y axes.

Is there such a thing as a "nodal rotation operator"?

Hello Emily,

We're a careful bunch here ; could you post the paragraph(s) so we get some context ?

Oh, I've just learned the author of my text has invented the term :) I knew that! It's an operator that rotates nodal lines, hence "nodal rotation operator" seems appropriate. Thanks!

## 1. What is a rotation operator on a sphere?

A rotation operator on a sphere is a mathematical function that describes the movement of points on a sphere as it rotates around a specified axis. It is commonly used in geometry and physics to model the behavior of objects in three-dimensional space.

## 2. How does a rotation operator on a sphere work?

A rotation operator on a sphere works by applying a rotation matrix to the coordinates of each point on the sphere. This matrix specifies the angle and direction of rotation around a specified axis. The resulting coordinates of the points after the rotation are used to create a new sphere with the same radius but at a different orientation.

## 3. What is the difference between rotation around the x-axis and rotation around the y-axis?

Rotation around the x-axis involves rotating the sphere horizontally, while rotation around the y-axis involves rotating the sphere vertically. This results in a different orientation of the sphere in each case.

## 4. How do rotation operators on a sphere affect the shape and size of the sphere?

Rotation operators on a sphere do not affect the shape or size of the sphere itself. Instead, they change the orientation of the sphere in three-dimensional space. The sphere remains the same size and shape, but its position and orientation are altered.

## 5. What are some real-world applications of rotation operators on a sphere?

Rotation operators on a sphere are commonly used in computer graphics, video game development, and animation to create realistic 3D objects. They are also used in physics and engineering to model the behavior of rotating objects and celestial bodies. Additionally, they have applications in navigation and astronomy for calculating the positions of objects in space.

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