Degrees of Freedom in Physics: Theory & Solutions

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SUMMARY

The discussion centers on the concept of degrees of freedom in physics, particularly in the context of analyzing mechanical systems. Participants emphasize the importance of understanding rotational dynamics and constraint equations as foundational knowledge. The independence of state variables allows for the summation of results from different degrees of freedom, leading to accurate overall outcomes. Resources such as Halliday, Resnick, and Krane's physics texts, as well as Wikipedia's entry on constrained motion, are recommended for further exploration.

PREREQUISITES
  • Understanding of rotational dynamics
  • Familiarity with constraint equations
  • Knowledge of state variables in physics
  • Basic principles of applied science
NEXT STEPS
  • Study Halliday, Resnick, and Krane's "Fundamentals of Physics" for foundational concepts
  • Research the Wikipedia article on "Fundamental equation of constrained motion"
  • Explore mathematical formulations related to degrees of freedom in mechanical systems
  • Investigate the principles of applied science and its relevance in engineering contexts
USEFUL FOR

Students of physics, educators teaching mechanical systems, and engineers applying theoretical concepts to practical problems will benefit from this discussion.

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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