Source of Difficult Newtonian Mechanics Problems?

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Discussion Overview

The discussion revolves around the search for sources of challenging Newtonian mechanics problems, with participants sharing recommendations for books and methods. The scope includes problem-solving resources, pedagogical approaches, and the comparison of different mechanics frameworks, such as Newtonian and Lagrangian mechanics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant expresses dissatisfaction with the Young and Freedman book, finding it superficial and not matching exam difficulty, and seeks alternative sources for harder mechanics problems.
  • Another participant recommends the book by Kleppner as a potential resource.
  • A suggestion is made to consider the problem book by Irodov and Krotov, noted for its difficult problems and availability for free.
  • Analytical Dynamics by E.T. Whittaker is mentioned as containing challenging problems.
  • David Morin's classical mechanics book is noted for having many difficult solved problems, though one participant cautions that it requires knowledge of Lagrangian mechanics, labeling it as "too hard."
  • There is a discussion about the utility of Lagrangian mechanics versus Newtonian methods, with some participants arguing that Lagrangian methods simplify force evaluations, while others assert that Newton's approach is necessary for determining forces in certain contexts.
  • A participant questions the applicability of Lagrangian methods to classical electrodynamics, prompting a discussion on the elegance of the Lagrange-Hamilton method for fields and its relation to symmetries and observable quantities.
  • Another participant challenges the ease of using Lagrangian methods for specific problems, asking for clarification on how to determine bearing forces at a pinned joint in an accelerating mechanism.
  • A final comment suggests that the problem posed could be addressed using Lagrange multipliers, indicating a potential application of Lagrangian methods to the scenario discussed.

Areas of Agreement / Disagreement

Participants express a variety of opinions on the effectiveness of different mechanics approaches, particularly regarding the Lagrangian versus Newtonian methods. There is no consensus on which method is superior for all scenarios, and the discussion remains unresolved regarding the best approach to specific problems.

Contextual Notes

Some participants note that certain recommended books may require prior knowledge of advanced topics, such as Lagrangian mechanics, which could limit their accessibility. Additionally, the discussion highlights the complexity of determining forces in mechanical systems, with various assumptions and conditions influencing the applicability of different methods.

Silicon-Based
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I'm looking for a source of harder mechanics problems, preferably with solutions. I'm supposed to use the Young and Freedman book, but I find it rather teadious and superficial; most problems don't match the difficulty and depth of the ones on the exam. I had my mid-term tests recently, and got startled seeing my dynamics score (63%), though math and relativity was a breeze (100% each), so I know that it isn't the math that hinders my progress. I study in the UK if that's relevant. Thank you.
 
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Go for Kleppner.
 
Silicon-Based said:
I'm looking for a source of harder mechanics problems, preferably with solutions. I'm supposed to use the Young and Freedman book, but I find it rather teadious and superficial; most problems don't match the difficulty and depth of the ones on the exam. I had my mid-term tests recently, and got startled seeing my dynamics score (63%), though math and relativity was a breeze (100% each), so I know that it isn't the math that hinders my progress. I study in the UK if that's relevant. Thank you.

Problem book by Irodov and Krotov has many difficult problems. They are also free.
 
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The text Analytical Dynamics by E.T. Whittaker has some real zingers!
 
classical mechanics david morin has lot of difficult solved problems. difficult for me anyways. it is 2nd year level.
 
password123 said:
classical mechanics david morin has lot of difficult solved problems. difficult for me anyways. it is 2nd year level.

I didn't recommend that book because it requires knowledge of Lagrangian mechanics. It is "Too Hard".
 
Mechanics without Lagrangians is hard. Whenever you've learned about the Action Principle, you'll not want to miss it again!
 
If your intention is to determine motion, Lagrange is often very useful. If your intent is to determine the force acting in a system, then Newton is the only option.
 
No, it is much easier to evaluate forces using the Lagrangian method than doing cumbersome free-body diagram analyses!
 
  • #10
vanhees71 said:
No, it is much easier to evaluate forces using the Lagrangian method than doing cumbersome free-body diagram analyses!
What about classical electrodynamics (if it's not too off-topic)? Is this classical field theory much easier with the Lagrangian (or Hamiltonian) approach?
 
  • #11
On a fundamental level the Lagrange-Hamilton method is also very elegant for fields. To "derive" classical electrodynamics you are almost forced to write down the correct Lagrangian by just knowing that the electromagnetic field is a massless gauge field. Then it's also easy to understand, why the observable quantities like energy, momentum and angular momentum of the fields are what they are, using Noether's theorem.

For practical calculations, of course you still have to solve the Maxwell equations. That's the same in mechanics: To finally find the trajectories of the particles in your given system, you have to solve the equations of motion, but often you can find an easier way by analyzing the symmetries and choose the most convenient coordinates.
 
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  • #12
vanhees71 said:
, it is much easier to evaluate forces using the Lagrangian method than doing cumbersome free-body diagram analyses!

If that is so, please describe for me how to get the bearing forces at a pinned joint in an accelerating mechanism. I look forward to being enlightened. (Please excuse the bold face, the button seems to be stuck!) I regularly use energy methods to get the system equation(s) of motion , but I know of no way to get the internal forces at joints and non-working forces at anchors (constraints) other than Newton.
 
  • #13
Isn't this a paradigmatic example for the Lagrange method of the first kind to be solved with Lagrange multipliers?
 

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