Classical Dynamics of Particles & Systems

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The discussion revolves around the derivation of equations related to the rotation of a coordinate system in classical dynamics. A user seeks clarification on why the projection of x2 on x'1 equals ab + bc and the relationship between vectors de and Of. Despite attempts to visualize the problem through various geometric methods, they are unable to prove their understanding. The conversation also touches on the significance of an asterisk in the problem statement, which indicates equivalence to Cartesian coordinates. Additionally, a user shares a diagram that aids in understanding the concepts discussed.
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?
 
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/
 
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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