(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

In rigid body, r is the position of a rigid body relative to world coordinates,

dr/dt is the rate of change of r in world coordinates.

I encountered the term Dr/Dt as the rate of change of r in world coordinates relative to the body coordinates system.

And that Dr/Dt = dr/dt-wxr

My question is, how does Dr/Dt is called? (terminology)

Also the operator D/Dt has the same rules as the operator d/dt, how do you proove it? There is some relationship to proove this, but what is this relation ship?

2. Relevant equations

Dr/Dt = dr/dt-wxr

3. The attempt at a solution

I tried to use Dr/Dt = dr/dt-wxr to proove that both operators has the same rules, but didnt succed.

In matter of fact, I found some contradiction.

For instance: d(AxB)/dt = Ax(dB/dt)+(dA/dt)xB

So D(AxB)/Dt = Ax(DB/Dt)+(DA/Dt)xB should also be true.

However using Dr/Dt = dr/dt-wxr showed that there is inequality.

Thank you.

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# Homework Help: Dr/Dt world coordinates problem

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