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Question:

So, I recently looked back into my physics textbook and found the concept of "impulse" there. Now, upon reading the explanation in the textbook and several definitions online, I noticed a vague and ambiguous definition for the concept. The definitions seemed confusing with the interlinkage of several topics such as "momentum" and "force" without actually clearing the difference between "the core idea" behind each topic.

Now, I wanted to know several things about the concept's emergence out of curiosity since I believe this could help build some context behind the concept.

  1. How is it that the "definition of impulse" evolved from being a term used interchangeably with force (as I found it in Sir Isaac Newton's "Philosophiæ Naturalis Principia Mathematica" and several other books) to a standalone concept?

  2. Is there any material that either provides perspective and usage of the concept without merging it with "force" and "momentum" or highlights an actual difference between between these similar concepts?

Note: I'm not really sure if it was meant to be (or is actually) a different concept at all. I saw someone mention that the emergence of impulse as a separate topic is a translation error from old times and it is not a standalone concept afterall. However, no evidence/source for it was presented. I couldn't really find much stuff related to impulse online highlighting it's emergence although I read somewhere else that it was a result of Huygens's approach of "analysis of impact" in kinematic terms.

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    $\begingroup$ Thank you everyone for taking time and answering! As the post is still active I think I'll take some time before accepting a particular answer, allowing for more answers. $\endgroup$ Commented Jun 21, 2024 at 18:10
  • $\begingroup$ Impulse : Momentum :: Work : Energy $\endgroup$ Commented Jul 19, 2024 at 4:13

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My best guess is that you are referring to this work.

Original:

English Translations:

Notice that Huygens uses the word impulse (in translation) to denote collision/impact. From collision properties rules are derived.

My apologies for this perhaps a bit tangential comment, but in German we still say "Impulserhaltung" for "conservation of momentum". So language dependent the connotation of an impulse is still used today.

P.S. On the question of the first use of the term “momentum” the following sources seems to credit Hamilton, and also has interesting exposition on the historical formation on the notion:

P.P.S.

An interesting historical source discussing the evolution of coinage and concepts together is Ernst Mach (1897) Die Mechanik in ihrer Entwickelung : historisch-kritisch dargestellt, Brockhaus where we find on page 272ff discussion of the evolution of both coinage and concepts. Going between the German original and English translation (E. Mach (1919) The Science Of Mechanics - Open Court) is itself very revealing.

The discussion starts as follows(p. 271ff):

Several of the formulas in the above-discussed The names equations have received particular names. The force formula? of of a moving body was spoken of by Galileo, who alternately calls it "momentum," "impulse," and "energy".

A very nice example of the language discrepancy is in Mach's discussion of Fourier's dimensional use of units vis-a-vis nomenclature. In the English translation we find (English p.279):

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with the German original (German p.279-280, in the original this table is split over two pages, I have merged it for ease of comparison):

enter image description here

There is much to be said here, but I will just talk about two: German "Antrieb" vs English "Impulse". While the roots for the notion of impulse (in English) is from impact collisions, the actual formula of it is valid for any duration, hence the force does not have to be impact-like at all but can be continuous. "Antrieb" (roughly "driving force" my translation) as used by Mach here is indeed a better word to capture this general notion. Mach uses "Bewegungsgrösse" (roughly "magnitude/unit of motion" my translation) for the English "momentum", which today we would call "Impuls" in German. Mach's nomenclature again is more descriptive than the modern usage, because in a sense conservation of momentum captures conservation of velocity (motion) if the mass is constant.

Regardless of these comments I suspect Mach will provide a rich source to answer many of the questions raised here, at least up to 1897.

P.P.P.S.

Given the interesting comments by Wrzlprmft and Conifold I would like to add a few more things, after some more investigating.

First off I do not recall ever having heard the term Kraftstoß in my German-language (Austrian) highschool and undergraduate physics courses (last mechanics course taken probably around 1991/2). This let me to dig a bit.

My best theory is that Kraftstoß is a back-translation from English textbooks (likely Tipler) that used that notion combined with uniformization pressures induced by the multilingual structure of wikipedia.

Compare this lecture notes by Marti (2001) who cites the German translation of Tipler (1994) Physik, Spektrum (disclaimer: I do not have access to this edition of Tipler so cannot verify the use of the word in it). I looked at numerous German textbooks over time and before 2005 I could not find any textbook with even the mention of the term. Some books introduced the word in revised editions some time after 2006 (Nolting, Fließbach, Meschede), but none gives the definition or has an index entry of it. In Nolting and Fließbach the term only appears as an undefined lose verbage in one exercise of computing forced excitations of a harmonic oscillator. My favorite is Meschede, Gerthsen Physik (2010/2015) which has a table of content and section heading "Impulse und Kraftstöße" but otherwise no discussion at all of the term and concept. None of these sources give the integral definition.

The term Kraftstoß appeared on wikipedia in 2007 and is immediately linked to notions of impulse in other languages including English. It appears to me that this is a relatively modern nomenclature emerging somewhere after Tipler's German translation and makes it onto wikipedia for a need to have translatability of terms across languages on the platform.

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  • $\begingroup$ A much more important point can be made about German, namely that the distinction between momentum and impulse doesn’t really exist – both translate to Impuls. You might find some people using distinct terms, in particular when working with material translated from English and other languages, but most physicists don’t really strictly separate the two (and it works just fine). $\endgroup$ Commented Jun 20, 2024 at 19:57
  • $\begingroup$ In German, English impulse is translated as Kraftstoß and is distinct from Impuls (momentum), it is similar in Russian. I think the OP is asking how the original concept of impulse (by whatever name) evolved from the change of momentum in collisions only, as in Huygens and Newton, to the general modern notion of analytical mechanics, as the integral of force over time. Was it Euler, d'Alembert, Lagrange, somebody later? $\endgroup$ Commented Jun 21, 2024 at 10:17
  • $\begingroup$ @Conifold: In German, English impulse is translated as Kraftstoß and is distinct from Impuls (momentum), … – I have studied physics in Germany and taught it to (in particular experimental mechanics). While I am aware that this term exists, it is barely used. Most people just use Impuls instead, which is also the colloquial term. $\endgroup$ Commented Jun 21, 2024 at 10:32
  • $\begingroup$ Regardless of the name use, how did the modern definition come up? $\endgroup$ Commented Jun 21, 2024 at 10:34
  • $\begingroup$ @Conifold Yes sir that is what I wanted to ask through this question. I more or less was asking about the the evolution of the definition as opposed to the name use. (also as a side note I just wanted to thank you for all your answers here on the site, it really is a treat going through all your answers) $\endgroup$ Commented Jun 21, 2024 at 18:03
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There is a good book which traces the historical details of concepts of mechanics such as momentum, impulse, quantiry of motion and energy. This story is very convoluted. Jennifer Coopersmith, Energy, the subtle concept, Oxford UP, 2015.

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