Can Someone Explain Non-English Text in This Image?

[CICCI_2011]

Hi best regard to all

This is my first post so forgive me in any mistakes.

If some one can explain to me those parts marked in red rectangles? It taught it was more convenient to post picture than typing. It's from a book that is not in English so I cut out parts with words. Many thanks to who ever have time to help me.

http://s1198.photobucket.com/albums/aa453/nikola5210/?action=view&current=Untitled.png"

 

[BruceW]

For the first red box, you need to use the expression from the previous line.
For the second red box, its simply a vector identity that is true for any general vector.

 

[I like Serena]

Hi CICCI_2011! Welcome to PF!

What you're looking at, are polar coordinates with local unit vectors.

If you have a body at a certain point, you can define a local cartesian coordinate system at that point.
One axis is in the direction of the point, the other axis is in the direction of the angle.
One of the corresponding unit vectors is named $\vec\rho_0$ in your text.
(Actually I'm used to naming it $\hat r$.)

When time passes, this point rotates with the angular velocity.
So a little time $dt$ later, $\vec\rho_0$ will point in a different direction.
The vector change is $\vec\omega \times \vec\rho_0 dt$.

There's for instance a wiki reference here: http://en.wikipedia.org/wiki/Vector_fields_in_cylindrical_and_spherical_coordinates

 

[CICCI_2011]

Thank you all very much for your response I really appreciate that.

I think I understand know.For first box This stands dP/dt=ω×P because P is rotating due to ω then dP/dt is perpendicular to ω and P so we can write dP/dt=ω×P.

For second box its vector identity like you wrote. Is it "Scalar product" (ω·P) and (ω·ω):

ω×(ω×P)=ω(ω·P)-P·(ω·ω)=ω|ω|·|P |cosα-P|ω|·|ω |cosα=
=ω·ω·P cosα-ω²·P=...

|ω|·|P |cosα=ω·P cosα

and

|ω|·|ω |cosα=ω·ω·1=ω² where angle between ω,ω is 0º cosα=cos0º=1

If not then what is it?

Sorry for this kind of typing but I can't change even color don know why.

You all helped a lot.

 

[I like Serena]

Yes. That looks right!

 

[CICCI_2011]

Thanks for your help and time, It's all clear now.

Best regards