# Can a Rigid Body's Rotation Be Described with Only Two Successive Rotations?

• Barkan
In summary, the conversation discusses the limitations of only performing two rotations (yaw and pitch) on a rigid body and how it affects the ability to describe the rotation of the body in the most general case. It is mentioned that while this still allows for pointing the camera in any direction, it is not possible to take a rotated picture of an object without a third rotation (roll). The motivation behind this discussion is to clarify the understanding of rotational movements in regards to rigid bodies.

#### Barkan

I try to clearify it as much as I can, and I greatly appreciate the given answers.

Suppose that we have a rigid body. We attach a movable coodinate frame on this body.

Normally, if I perform 3 successive rotations such as Z-Y-X or Z-Y-Z (or any other 24) I can describe its rotation in the most general case.

If I perform only two rotations what will happen then? Let's suppose I only perform a Z-Y rotations (first rotate about yaw then rotate about the current pitch) what would be the loss in terms of generality? Let's say, without the 3rd successive rotation, I cannot describe the half of the ... plane and/or sphere?

Thank you very much in advance.

So you only have yaw and pitch, but no roll. Camera tripods rotate this way. You can point the camera in ANY direction, so you're not limited there. However, you cannot point the camera at an object and then roll the camera to take an upside-down picture for example. That's what you lose by only having two rotations.

If this doesn't help any, do you think you can clarify the question? What is the motivation (what exactly are you trying to do?)

I made a small mistake in my previous post. You could actually take a picture in any direction upside-down. You would do this by yawing so that you're pointing in the opposite direction, then pitching the camera so that it's inverted to look at the object.

So 0 degrees and 180 degrees are special cases. In general, you cannot take a rotated picture of an object.

## What is rotational motion?

Rotational motion, also known as angular motion, is the movement of an object around an axis or center point. It is a type of motion that involves both translation and rotation.

## What is a rigid body?

A rigid body is an object that maintains its shape and size even when it is subjected to external forces. It does not deform under the influence of these forces, and all of its particles move in the same manner.

## What is angular velocity?

Angular velocity is a measure of how fast an object is rotating around an axis. It is defined as the change in angular displacement over time and is typically measured in radians per second.

## What is the moment of inertia?

The moment of inertia is a measure of an object's resistance to changes in its rotational motion. It depends on the mass, shape, and distribution of mass of the object. Objects with a larger moment of inertia require more torque to achieve the same angular acceleration.

## How is rotational motion related to linear motion?

Rotational motion and linear motion are two types of motion that are interconnected. In rotational motion, an object moves in a circular path around an axis, while in linear motion, an object moves in a straight line. However, rotational motion can be broken down into linear motion components, and vice versa, using trigonometric functions.