Discover the Fascinating Concept of Rotation Around a Curve

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The concept of rotation around a curve involves a body rotating along a non-linear path, which challenges the idea of rigidity. Unlike rotation around a straight line, this type of motion suggests that the body must adapt to the curvature of the path. The discussion highlights the moon's rotation around the Earth as a practical example of this phenomenon. This type of rotation raises questions about the physical properties of the rotating body. Understanding these dynamics can deepen insights into celestial mechanics and motion.
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Can you imagine rotation of a body around a curve? I said a curve and I didn't mean a straight line of course.
 
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such a body won't be rigid i guess. otherwise it will have to be the same curve as the one around which it is rotating.
 
Yes, I can imagine the moon's rotational about the earth..
 
I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
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