# Manuscript on elementary rigid-body dynamics

• I
• vanhees71
In summary, the conversation discussed an elementary introduction to rigid-body dynamics, specifically focusing on the force-free and heavy symmetric top. The conversation also brought up the cases of ##p_\psi=\pm p_\varphi## and the non-uniqueness of Euler angles when ##\theta\ne 0\pmod{\pi}##. The speaker agreed to consider these cases and added a sentence to address the non-uniqueness of Euler angles for ##\vartheta \in \{0,\pi\}##.
vanhees71
Gold Member
2023 Award
In view of questions occurring from time to time in this forum, I've written an elementary introduction to rigid-body dynamics (mostly about the force-free and the heavy symmetric top). I hope, it's of some use:

https://itp.uni-frankfurt.de/~hees/pf-faq/spinning-top.pdf

weirdoguy, ergospherical, wrobel and 3 others
Nice text. As for section "The heavy symmetric top" what about to consider the cases ##p_\psi=\pm p_\varphi##.
Perhaps it would also be good to stress that the Euler angles are correctly defined when ##\theta\ne 0\pmod{\pi}##

vanhees71
That's an interesting case, I guess. I'll have a look at it. I've put a sentence concerning the non-uniqueness of the Euler angles for ##\vartheta \in \{0,\pi\}##.

wrobel

## 1. What is a manuscript on elementary rigid-body dynamics?

A manuscript on elementary rigid-body dynamics is a written document that outlines the basic principles and laws governing the motion of rigid bodies, which are objects that maintain their shape and size even when subjected to external forces. It typically includes mathematical equations and diagrams to explain the concepts and may include examples or applications of these principles.

## 2. Who is the target audience for a manuscript on elementary rigid-body dynamics?

The target audience for a manuscript on elementary rigid-body dynamics is typically undergraduate or graduate students in physics, engineering, or related fields. It may also be useful for researchers or professionals who need a refresher on the fundamental concepts of rigid-body dynamics.

## 3. What topics are typically covered in a manuscript on elementary rigid-body dynamics?

A manuscript on elementary rigid-body dynamics may cover topics such as kinematics (the study of motion without considering its causes), dynamics (the study of motion and its causes), Newton's laws of motion, conservation of momentum and energy, rotational motion, and oscillations. It may also cover applications of these principles, such as in engineering or biomechanics.

## 4. How is a manuscript on elementary rigid-body dynamics different from a textbook?

A manuscript on elementary rigid-body dynamics is typically a more concise and focused document compared to a textbook. It may be written by a single author or a small group of authors, whereas a textbook is often written by a team of authors and covers a wider range of topics. Additionally, a manuscript may not include exercises or practice problems like a textbook does.

## 5. Are there any prerequisites for understanding a manuscript on elementary rigid-body dynamics?

A basic understanding of calculus and physics is typically required to understand a manuscript on elementary rigid-body dynamics. It may also be helpful to have a familiarity with vector algebra and basic mechanics concepts. However, some manuscripts may include a brief review of these topics to refresh the reader's understanding.

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