Impulsive Tension: Debunking Its Usefulness in Calculating Momentum Change

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The term "impulsive tension" is debated regarding its appropriateness in calculating momentum change. Impulsive forces are typically defined as non-zero forces acting over a very short duration, making instantaneous measurement impractical. In the context of tension, this concept can be applicable, particularly when considering scenarios like a quick pull on an ideal wire attached to a body. The discussion emphasizes that while impulsive tension may aid in calculations, its classification remains contentious. Overall, the utility of impulsive tension in momentum change calculations warrants further examination.
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is it appropriate to call a term impulsive tension or is it just useful for calculation of change of momentum?
 
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usually you call impulsive a force that is non zero for such a short time that it is impractical (or impossible) to measure instant by instant so you have to rely on its impulse that is the change of momentum of what it acts on. For a tension this could be appropriate e.g. an ideal wire is attached to a body and you give it a quick pull and let go of the wire

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Thread 'Derivation of Hamilton's Principle: Questions'

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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