I think it is definitely the case that most physicists have quite a wrong picture of past physics.
I have some historical information about the work of Joseph Louis Lagrange. (I don't think it affects the thrust of your post.)
An english translation of Lagrange's 'Mecanique Analytique' is available on Archive.org. Analytic mechanics Lagrange used calculus of variations for problems in statics, but not for problems in mechanics.
At the time the action concept that was available was Maupertuis' action. (Hamilton's action was introduced by William Rowan Hamiltons in 1834, Lagrange died in 1813) In his work 'Mecanique Analytique' Lagrange offers the opinion that Maupertuis' action is not particularly relevant. Quoting one sentence from page... (read more)
I think it is definitely the case that most physicists have quite a wrong picture of past physics.
I have some historical information about the work of Joseph Louis Lagrange. (I don't think it affects the thrust of your post.)
An english translation of Lagrange's 'Mecanique Analytique' is available on Archive.org. Analytic mechanics Lagrange used calculus of variations for problems in statics, but not for problems in mechanics.
At the time the action concept that was available was Maupertuis' action. (Hamilton's action was introduced by William Rowan Hamiltons in 1834, Lagrange died in 1813) In his work 'Mecanique Analytique' Lagrange offers the opinion that Maupertuis' action is not particularly relevant. Quoting one sentence from page... (read more)