Degrees of Freedom in Physics: Theory & Solutions

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Discussion Overview

The discussion revolves around the concept of degrees of freedom in physics, particularly in the context of mechanical systems. Participants explore the theoretical background and mathematical formulation related to analyzing systems with multiple degrees of freedom, including the implications of combining results from independent quantities.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • One participant seeks information on the theoretical background for analyzing degrees of freedom in mechanical systems and questions the validity of summing quantities to obtain results.
  • Another participant suggests a reference to a textbook (Halliday, Resnick, Krane) for foundational concepts.
  • A participant emphasizes the importance of understanding rotational dynamics and constraint equations in this context.
  • There is a discussion about the independence of the quantities involved in degrees of freedom, likening it to solving for x and y positions of an object in space.
  • Multiple participants express a desire for detailed discussions and mathematical formulations regarding the topic.
  • A suggestion is made that the term "Applied Science" may relate to the application of formulas in engineering contexts.

Areas of Agreement / Disagreement

Participants express varying levels of familiarity with the topic, and while some provide references and insights, there is no consensus on a specific approach or solution to the original inquiry.

Contextual Notes

Some participants reference specific educational materials and concepts, but there is an absence of detailed mathematical steps or definitions that could clarify the discussion further.

Who May Find This Useful

This discussion may be useful for students and educators interested in the theoretical and practical aspects of degrees of freedom in mechanical systems, as well as those seeking resources for further study in physics and engineering.

chimay
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Hi,

in my previous course on basic Physics we learned to solve problems concerning simple mechanical systems like this:

2 gradi.png

The method consists in analyzing separately the two degrees of freedom of the system, computing for each degree the acceleration of each body (or whathever) and the sum both of them to obtain the overall result.
Can someone tell me where I can find information about this approach? What does assure me that the sum of the quantities give me the correct result? I would like to understand in detail where the theoretical backgroud lies.

Thank you.
 
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PHYSICS
halliday resnick krane vol 1
 
you need to understand rotational dynamics for this and also constraint equations
 
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Halliday, Resnik? Boy, that brings memories from several decades ago...but not enough to know what the OP is talking about...

...then again, simply from the "degrees of freedom" point of view, the reason why you can combine the results is precisely because these two quantities are independent from each other...otherwise, they wouldn't be degrees of freedom...it is like solving for the x position AND the y position of an object and combining the two quantities to know exactly where the object is in space.

Does this help?

keywords: degrees of freedom, state variables.
 
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Thank you, very helpfull.

Where can I find quite a detailed discussion about these topics?
I am looking for a general approach of this kind and its mathematical formulation.

Thank you a lot
 
chimay said:
Thank you, very helpfull.

Where can I find quite a detailed discussion about these topics?
I am looking for a general approach of this kind and its mathematical formulation.

Thank you a lot

Would it be that you are looking for the term, "Applied Science", the application of formulas for specific uses found in engineering.

Applied Science
https://en.wikipedia.org/wiki/Applied_science
 
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