Degrees of Freedom in Physics: Theory & Solutions

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The discussion centers on understanding the concept of degrees of freedom in physics, particularly in mechanical systems. Participants emphasize the importance of analyzing independent degrees of freedom to compute overall system behavior accurately. They reference foundational texts like Halliday, Resnick, and Krane for theoretical background and mathematical formulation. The conversation also touches on the relationship between independent variables and the ability to combine results for comprehensive analysis. Resources such as Wikipedia are suggested for further exploration of constrained motion and applied science.
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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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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