The motion of cats and stuff in free fall

[etotheipi]

Hey everyone, where can I learn fairly rigorousoly about continuum mechanics and specifically about how to map between motions in the configuration space $\mathcal{C}$ and motions in the shape space $\mathcal{C} / SO(3)$? I would like to model the general motion of deformable bodies with constant angular momentum about the mass centre, thanks!

 

[Frabjous]

This does not go to where you want to go, but I think it would show you where non-linear solid mechanics would start

https://my.mech.utah.edu/~brannon/public/rotation.pdf

Rebecca turned it into a book 16 years later

Rotation, Reflection and Frame Changes by Brannon

https://www.amazon.com/dp/0750314524/?tag=pfamazon01-20

 

[Frabjous]

From the publishers site

Frontmatter
https://iopscience.iop.org/chapter/978-0-7503-1454-1/bk978-0-7503-1454-1ch0.pdf

Introduction
https://iopscience.iop.org/chapter/978-0-7503-1454-1/bk978-0-7503-1454-1ch1.pdf

The rest are behind a paywall.

Check out the description of Chap 24
“Chapter 24 returns to the problem of deformable media, but considers the case that bulk rigid motion is the primary motion, with relatively small deformations with respect to an appropriately defined rigidly moving observer frame (e.g., turbine blade, human bodies in a braking automobile, etc). Phantom body forces are derived to allow solving the problem in a non-inertial material frame.”

24 Pseudo-body force for spinning problems 24-1
24.1 Kinematics of superimposed rotation (general analysis) 24-1
24.2 Fiducial body force for superimposed rigid motion 24-7
24.2.1 Special case: pure accelerated translation 24-8 (without rotation)
24.2.2 Special case: centrifuge (steady rotation 24-9 without translation)
24.2.3 Buried explosives 24-11
Reference 24-12

Sounds like your cat dropping experiment.

 

[etotheipi]

I did also find some notes here, which at a glance look alright:
https://web.mit.edu/abeyaratne/Volumes/RCA_Vol_II.pdf

not sure if there's anything about spinny cats in them, though! I'm afraid, I'm probably going to have to put the whole modelling various animals in free-fall thing on hold for the moment, because I have write-ups due tomorrow