# How did Lagrange get his equation (the so-called Euler-Lagrange equation)

The variational principle is named after Hamilton, instead of Lagrange.

So it seems that he did not derive his equation by the variational method.

• Possible duplicate of who was the first to discover the Hamilton principle of classical physics? – Francois Ziegler Apr 13 '18 at 3:05
• @FrancoisZiegler This question appears to be a "how" question, not a "who" question. – Geremia Apr 13 '18 at 3:11
• @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.) – Francois Ziegler Apr 13 '18 at 3:31
• @FrancoisZiegler Yes, Euler can claim priority over Lagrange in its derivation. (In fact, Santilli 1978 p. 10 cites Euler 1736.) – Geremia Apr 13 '18 at 15:42