Is Motion Scalar or Vector in Nature?

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Motion is debated as being scalar, vector, or neither, with some arguing it is not quantifiable. While velocity, momentum, and kinetic energy can be measured, motion itself lacks a numerical value. A definition of motion suggests it is a complex, time-dependent mapping from phase space to phase space. The term "quantifiable" refers to the ability to assign a numerical value to a concept. The discussion highlights the complexity of understanding motion beyond simple classifications.
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Is Motion a scalar or vector or neither?
 
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Motion is not something even quantifiable. You can say a system has a higher velocity, or more momentum or more kinetic energy, but not more motion.
 
excuse me, what do you mean by quantifiable?
 
One definition of motion I have seen is a time-dependent map from phase space to phase space. Which is quite a bit more complex than scalar vs vector.
 
'quantifiable' = capable of having a number, or quantity, assigned to it.
 
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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