The variational principle is named after Hamilton, instead of Lagrange.
So it seems that he did not derive his equation by the variational method.
$\begingroup$
$\endgroup$
4
-
1$\begingroup$ Possible duplicate of who was the first to discover the Hamilton principle of classical physics? $\endgroup$– Francois ZieglerApr 13, 2018 at 3:05
-
$\begingroup$ @FrancoisZiegler This question appears to be a "how" question, not a "who" question. $\endgroup$– GeremiaApr 13, 2018 at 3:11
-
1$\begingroup$ @Geremia The other question asks “what exactly, was Lagrange’s role?”, and this is thoroughly answered in the quoted paper of Fraser (1983, p. 217); also (1985, p. 173), where $\frac d{dt}\frac{\partial T}{\partial\dot q_i}-\frac{\partial T}{\partial q_i}$ is traced to 1764, 24 years before the Mécanique Analytique. (Your answer would fit there just as well.) $\endgroup$– Francois ZieglerApr 13, 2018 at 3:31
-
$\begingroup$ @FrancoisZiegler Yes, Euler can claim priority over Lagrange in its derivation. (In fact, Santilli 1978 p. 10 cites Euler 1736.) $\endgroup$– GeremiaApr 13, 2018 at 15:42
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
Lagrange derived it in his Méchanique Analytique. Dugas summarizes it in his History of Mechanics pp. 342-344:
