# History of rotational / rigid body mechanics

In teaching introductory mechanics classes, I like to give my students a much-abridged sketch of some history of mechanics, starting with Aristotle and ending with Galileo and Newton. Most of the introductory physics texts I've seen contain at least a cursory treatment of this story.

However, I've never seen similar discussion of the history of rotational kinematics or dynamics anywhere. I once had a student ask whether what we call "Newton's law for rotation" was due to Newton, and I had to admit that I had no idea. I'm hoping that someone can give me an outline of the development of rotational mechanics, including things like:

• Kinematic description of rotational motion in terms of angular displacement, angular velocity, and angular acceleration
• Torque
• The relationship between angular acceleration and torque
• Moment of inertia

I'd also be interested to know how much of this "Physics 101" treatment of rigid body motion preceded the more sophisticated description of rigid body mechanics with Euler equations, moment of inertia tensor, etc.

• Rotation of a rigid body does not fit in your specified time period, "between Archimedes and Galileo/Newton". It is of a later origin, and the key founding author is Euler. Even the kinematic was not fully developed until the end of 19 century (Klein, Sommerfeld). Some other key names are Lagrange, and Poisson, – Alexandre Eremenko Apr 1 at 0:40
• Roberson and Schwertassek give a brief survey of the history of rotational mechanics in the introductory parts of Dynamics of Multibody Systems. – Conifold Apr 1 at 1:01
• @AlexandreEremenko Thanks for your comment, but that part was just context/motivation. The time period involved is irrelevant to me. – d_b Apr 1 at 17:36
• @Conifold Thanks, I'll take a look at that. – d_b Apr 1 at 17:36

In my opinion: Euler did so much already that the contributions from later physicists/mathematicians are at a level of abstraction that is beyond the scope of standard physics courses.

Among the subjects not already covered by Euler, I assume, is the quite unique case of the intermediate axis theorem. Arguably awareness of that phenomenon took off only because of the video recorded on a space station showing a demonstration of the motion of a rigid body with three different moments of inertia

The equations for that case are known, numerical simulations reproduce the motion. But will a textbook author include a section about the intermediate axis theorem? I doubt it; even the minimum mathematics to treat the case is already very abstract.
(Also, in order to move according to the idealized model the object must be perfectly rigid. But in the real world there is no such thing as perfect rigidity. Any mechanism that can dissipate kinetic energy will dissipate kinetic energy.)

So, in the end: the part of rotational mechanics that makes it into physics textbooks has a short history: it's Euler.

As to development of rotational mechanics prior to Euler:

Newton had inferred that since the Earth is rotating it will have an equatorial bulge. Because of that non-spherical shape the center of gravitational attraction does not coincide with the center of mass. (The two coincide only in the case of a perfectly spherical celestial body.) As a consequence the gravity of the Sun exerts a torque on the Earth, and so does the gravity of the Moon. Newton had arrived at the view that the precession of the equinoxes was due to this combined torque effect from Sun and Moon.

The interpretation must be that Newton had anticipated the concept of gyroscopic precession. Not a generalized concept of gyroscopic precession, but a concept specific for the Earth precession. In the Principia Newton offers a calculation.

The outcome of Newton's calculation matches the actual precession of the equinoxes quite well, but historians of science state that the accuracy of the data that Newton was working with was certainly not good enough to be that succesful. There is a question here on HSM about that Was Newton's succesful calculation of precession of equinoxes a fluke?

Most of the Principia was later restated in the form of differential calculus. It was that more accessible form that spread throughout the physics community. It would appear: on the subject of the precession of the equinoxes Newton's description in the Principia was not enough to reconstruct his thought process. So it appears that on that subject there was no follow-up.

The notion of moment is important in rigid body dynamics. Historically speaking, this was pioneered by Archimedes in his Method where he outlined his theory of the lever.

It's worth adding that the parallelogram of forces/velocities was pioneered in the work known as Mechanica, traditionally thought to be Aristotle, but now thought to be by a student of his school, possibly Achytas. It was also an influence on Archimedes.