Body-Fixed Reference Frame -- How is it useful?

Hello Everyone,
I am trying to understand the usefulness of a body-fixed (body-centered) frame of reference ##O'x'y'z'## versus a lab frame of reference ##Oxyz##. The body-fixed frame is attached to the moving body and changes orientation exactly as the body changes orientation. From the perspective of an observer sitting at ##O'## and using to the body frame ##O'x'y'z'## to describe the body's motion, the body does not move at all and nothing changes... On the other hand, the ground, lab-based reference frame ##Oxyz## is obviously useful since the body moves a relative to it and we can determine its position, velocity, etc.

Why would we use a body-frame at all? The rigid body under consideration is composed of many points. I guess we can describe the overall motion of the body by looking at how the body-fixed frame attached to it changes relative to the frame ##Oxyz##. Is that the reason why we use ##Ox'y'z'##?

Thanks

A body fixed frame is extremely useful in kinematics of rigid bodies such as a four bar linkage. The position of any point on the coupler link is easily described in a body coordinate system, and this facilitates the determination of the locus of that point in the global frame.

The body frame is also useful for describing the geometry of a body (rigid or deformable). This is important for calculating the center of mass location and the several mass moments of inertia.

Dr.D said:

A body fixed frame is extremely useful in kinematics of rigid bodies such as a four bar linkage. The position of any point on the coupler link is easily described in a body coordinate system, and this facilitates the determination of the locus of that point in the global frame.

The body frame is also useful for describing the geometry of a body (rigid or deformable). This is important for calculating the center of mass location and the several mass moments of inertia.

Thank you!

So, a moving rigid body is formed by many points. Considering a specific point ##A## on the body, I see how its position ##r_A## can be described as a vector either from ##Oxyz## or from ##O'x'y'z'##, the body centered frame. From the body fixed frame, the vector ##r_A## connects the origin ##O'## to the point ##A## and does not change in time. From the lab frame, on the other hand, the position of point ##A## changes with time...

I still don't appreciate the gain we get from describing points' positions from ##O'x'y'z'##

Are you familiar with the slider-crank mechanism, the basic mechanism used in IC engines? Assuming that you are, think about the connecting rod center of mass. What is the path of that center of mass as the crank turns? What are the velocity and acceleration of that CM? These questions are very difficult to address directly in the global system, but they are not difficult if a body coordinate system is used.

In a more prozaic context, most airplane pilots prefer body-centered coordinates when flying their craft.

hutchphd said:

In a more prozaic context, most airplane pilots prefer body-centered coordinates when flying their craft.

Do you mean to tell me that airplanes in Australia aren't flying upside down? LIES!