My question is not homework. I feel ashamed of having this doubts but I'm really stuck on this.(adsbygoogle = window.adsbygoogle || []).push({});

The problem is I have a reference frame xyz and here I define the COM [itex]\vec x{_{cm}}[/itex] of the system.

Now I move the COM reference frame x'y'z':

[itex]\vec{x'}=\vec{x}-\vec x{_{cm}}[/itex]

In this reference frame I define a new orthonormal system x''y''z'' centered in (0,0,0), i.e. the COM mass.

I now want to recover to component of my last orthonormal system x''y''z'' in the original system xyz.

If I do:

[itex]\vec{x''}{ {\rm (in~ xyz)}}=\vec{x''}{ {\rm (in~ x'y'z')}}+\vec x{_{cm}}[/itex]

I don't recover an orthonormal system of axis! What is wrong in my method?

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# How to trasform an orthonormal system in two reference frames

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