Classical Dynamics of Particles & Systems

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Discussion Overview

The discussion revolves around the Classical Dynamics of Particles & Systems, specifically focusing on the derivation of equations related to the rotation of a coordinate system. Participants are exploring the mathematical relationships and geometric interpretations involved in these equations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant expresses understanding of certain equations but seeks proof for the projection of x2 on x'1 being equal to ab + bc, indicating a need for geometric validation.
  • The same participant questions the equivalence of vector de to vector Of, highlighting a struggle with visualizing and proving these relationships through various mathematical approaches.
  • Another participant inquires about the meaning of an asterisk in the problem statement, suggesting a need for clarification on notation.
  • One participant suggests checking the errata for the book referenced, indicating that there may be relevant corrections or clarifications that could assist in understanding.
  • There is a clarification that x1, x2, and x3 are equivalent to x, y, and z in the Cartesian plane, addressing a potential misunderstanding about the notation used.
  • Participants share links to diagrams that may aid in understanding the concepts discussed, with one participant confirming the usefulness of a shared diagram.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the specific proofs sought by the initial poster. There are multiple inquiries and suggestions, but no definitive answers or resolutions to the questions raised.

Contextual Notes

Participants reference different sources and errata, indicating that there may be discrepancies or additional context needed for the material being discussed. The discussion is self-directed and not tied to formal homework assignments.

Who May Find This Useful

This discussion may be of interest to students or self-learners studying classical dynamics, particularly those grappling with geometric interpretations and mathematical proofs in the context of coordinate transformations.

Dr_Pill
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This is an image of Classical Dynamics of Particles & Systems, chapter 1

In deriving the equations for the rotation of a coordinate system

wuNFqPU.jpg


I understand the equations 1.2a & 1.2b b, but why is the projection of x2 on the x'1 equal to ab +bc

and why is the vector de equal to the vector Of?

I tried the whole afternoon drawing triangles, writing vectors as one another, cosinus,sinus rules, congruent triangles everything I could think off, yet I can't prove it.
It seems obvious, but I want proof :D

(how to resize my image)

(btw, this is self-study, no homework or anything like that)
 
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What does the asterisk in the problem statement indicate?
 
Stephen Tashi said:
I don't know the answers to your questions. It's worth reading the errata for the book, even if it isn't relevant to this particular problem: http://astro.physics.sc.edu/Goldstein/

It's not Goldstein. But from Marion Jerry, but ok, will check errata.

sapratz said:
What does the asterisk in the problem statement indicate?

Just saying that x1,x2,x3 are equivalent to x,y,z in the Cartesian plane.
 

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