# English translation of Helmholtz' paper: “On the Physical Significance of the Principle of Least Action”

Ueber die physikalische Bedeutung des Princips der kleinsten Wirkung. Journal für die reine und angewandte Mathematik (Crelle's Journal), Volume 100, Issue 2, 1887, Pages 137-166, and Volume 100, Issue 3, 1887, Pages 213-222.

The title in English: On the Physical Significance of the Principle of Least Action.

Has it ever been translated (to English)?

• I just took a quick look at the paper, and the notation is funny - the same letters are used, but with different meanings: the coordinates are $p$ instead of $q$, which in turn is used for the velocities $\dot q$; momenta are $c$ instead of $p$, potentials are $F$ instead of $V$, the Lagrangian is called $H$ and has the opposite sign, ie corresponds to $-L$; kinetic energy is called $L$ instead of $T$; the Hamiltonian is called $H'$ instead of $H$ – Christoph Apr 29 '13 at 13:42
• Hi @Gugg. I think the German spelling mistakes (when compared to modern German) in the original German title will generate an endless edit war. Perhaps one should display both the original and a grammatically correct German title? (Also note that Helmholtz spells 'Prinicips' with 3 i's!) – Qmechanic Apr 29 '13 at 18:03
• @Qmechanic Hmmm,... NO. :) I think there are no spelling mistakes in the original title. At the time, they were using both Ue's as well as u-umlauts (see the paper itself), but apparently only Ue's in titles. Also "Princips" had been converted to modern-day German (although my German is lousy). The current version proved to be much more useful in Internet search. That is, the misspelling/modernization made it more time-consuming. Also, I don't expect an edit war. Almost certainly, I won't participate. – Keep these mind Apr 29 '13 at 18:20
• @Qmechanic To your edited comment. The 3 i's: Not in the title, he doesn't. Does he? – Keep these mind Apr 29 '13 at 18:27
• @Glen The Udderboat: Ups, you're right. That's just a typo of the website. – Qmechanic Apr 29 '13 at 18:30