# When to consider body fixed reference frame

• curiousPep
In 2D cases, it may be easier to use a fixed reference frame that is not attached to the body, but in 3D cases, a body fixed reference frame may be more suitable for analyzing the motion of a complex rigid body.
curiousPep
TL;DR Summary
I am a bit confused when to use the Euler equations and consider body fixed reference frame and when to just consider a fixed reference frame
Hello I am studying mechanics and I have been reading about having the reference frame fixed at a certain point, body fixed and also the gyro equations.
I an identify the gyro case easily as I am looking for an AAC body which rotates about an axis.
I am confused about the other two cases in which types of problems I should apply a body fixed reference frame.
What I understand in 2D it's easier not to use the body fixed reference frame. However, I am not that sure for 3D cases
Can someone give me an example or an explanation, thank you.

A body fixed reference frame is used when you want to describe the motion of a rigid body. In this case, the reference frame is attached to the body and its axes are rotated with the motion of the body. For example, if you are analyzing the motion of a car, you could use a body fixed reference frame in which the x-axis is along the length of the car and the z-axis is perpendicular to the ground. Using this reference frame, you can derive the equations of motion for the car and analyze its behavior.

## 1. When should a body fixed reference frame be used?

A body fixed reference frame should be used when studying the motion or behavior of a specific object or body. It allows for a more accurate and detailed analysis of the object's movement and position in space.

## 2. What are the advantages of using a body fixed reference frame?

Using a body fixed reference frame allows for a more simplified and precise analysis of an object's motion. It also eliminates the need to consider external forces or reference points, making calculations and measurements more straightforward.

## 3. How is a body fixed reference frame different from an inertial reference frame?

An inertial reference frame is a non-accelerating frame of reference, while a body fixed reference frame is attached to a specific object and moves with it. This means that an inertial reference frame can be used for studying the motion of multiple objects, while a body fixed reference frame is only applicable to one object.

## 4. Can a body fixed reference frame be used for all types of motion?

No, a body fixed reference frame is most suitable for rotational or circular motion. For linear motion, an inertial reference frame is more appropriate.

## 5. How do you choose the origin and axes of a body fixed reference frame?

The origin and axes of a body fixed reference frame are typically chosen to be at the center of mass and aligned with the object's principal axes of rotation. This allows for a more accurate and simplified analysis of the object's motion.

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