Classical Dynamics of Particles & Systems

[Dr_Pill]

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

In deriving the equations for the rotation of a coordinate system

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)

 

[sapratz]

What does the asterisk in the problem statement indicate?

 

[Stephen Tashi]

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/

 

[Dr_Pill]

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.

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.

 

[Stephen Tashi]

Is this diagram better: ?
http://anorganik.uni-tuebingen.de/klaus/nmr/index.php?p=conventions/euler/rotation

 

[Dr_Pill]

Is this diagram better: ?
http://anorganik.uni-tuebingen.de/klaus/nmr/index.php?p=conventions/euler/rotation

Yes!

Thank you. :)