# Stationary/inertial reference frame

In Modern Robotics by Kevin Lynch, there is a term "stationary" frame, but this is never defined. Googling shows that this is synonymous with inertial frame.

Apparently inertial frame means rigidly attaching an accelerometer to a frame would show that the frame has 0 acceleration.

However, in Modern Robotics, it says body frames, which are attached to moving objects, are also inertial frames. How is this possible? If the body frame is attached to a baseball bat, and our robot swings the bat, won't the frame undergo acceleration?

Due to the way that frames are defined in the Modern Robotics book (and in this type of vector-field mechanics in general, such as those of Featherstone), both the spatial frame and the body frames are defined as stationary inertial frames. This requires a bit of a different conceptual understanding than the more traditional moving frames that have been "attached" to moving bodies in most dynamics textbooks.

As stated in the MR quote in the answer by JJB_UT, the body frames that are used to perform calculations at each instant in time are defined as the stationary inertial frames that are in the same pose (position and orientation) as the more classic moving body frames might be at that same instant. This key difference is what enables a lot of the simpler math in MR compared to other dynamics textbooks and notations.

Cheers, Brandon

• I do not understand what this adds to my answer. Cheers Commented Jan 25, 2021 at 19:25
• Your first statement is misleading by claiming that dynamics are not being considered. In fact, these spatial and body frames are used for kinematics, dynamics, and all other mechanical computations in the Modern Robotics textbook. You also erroneously claim that the frames are attached to the bodies and just "frozen in time", which they are not. The frames are stationary inertial frames that are chosen at each instant to be coincident to the traditional moving frames seen in other books. This is a key advantage of this formulation, by eliminating any and all effects due to moving frames. Commented Jan 25, 2021 at 21:02

The frames are considered inertial because we are not considering "dynamics" (read: acceleration). Essentially, as far as my experience goes with MR, all the math around frames in the book considers that you are momentarily frozen in time, "viewing" that state of the frame at that instantaneous time. Because of this it is considered stationary and therefore inertial.

I am no expert on the matter so I'd love to hear feedback on my answer!

From Chapter 3 Page 59 of MR:

All frames in this book are stationary, inertial, frames.When we refer to a body frame{b}, we mean a motionless frame that is instantaneously coincident with a frame that is fixed to a (possibly moving) body. This is important to keep in mind, since you may have had a dynamics course that used non-inertial moving frames attached to rotating bodies. Do not confuse these with the stationary, inertial, body frames of this book.

• @user3180 did this not answer your question? Commented Jan 15, 2021 at 13:45
• I don't think this does answer the question, as the stationary inertial body frames in this book are used to support kinematics, dynamics, and many other mathematical calculations. Commented Jan 19, 2021 at 19:27