Unfortunately there are tons of books about the history of physics that get many details wrong, because apparently the authors have not actually read many of the primary sources, especially when they had not been written in English, but in German, French, Latin or other languages.
Even the original works written in English, like those of Hamilton, pose serious problems when you are not careful, because many words used in physics have changed in meaning during the time, some of them multiple times (e.g. "energy", "action" or "force"). Those who are not aware of this frequently reach wrong conclusions about who has said what.
A few authors have actually read the primary sources, but those typically do not understand physics so well as to be able to distinguish the important concepts from those of little importance, so they are not able to trace the evolution of the important concepts :-(
The only foolproof method to understand the history of physics is to read very carefully the original works (carefully, because the words and the notations used may be very different from those used now). Fortunately, that has become much easier now than before, because there are many online repositories with digitized scientific works from the previous centuries.
For example, "Sir William Rowan Hamilton (1805-1865): Mathematical Papers":
The most important for this thread are (especially the 2nd, which introduces the modern Lagrangian formulation):
1834-04: “On a General Method in Dynamics”, and
1834-10 (but published in 1835): “Second Essay on a General Method in Dynamics”.
The first who has shown how to rewrite the second order system of Lagrange equations into the first order system of equations now called Hamilton's equations (i.e. by using the equivalent of the Legendre transformation) was Poisson in 1809, but the last time when I have searched for that work online I could not find it.
After Poisson, Cauchy has presented in 1831 a method equivalent with that published by Hamilton in 1835. I also could not find online the 1831 work, but an extract of it has been republished in 1837 and this can be found online in many places, for instance at:
Note sur la variation des constantes arbitraires dans les problèmes de Mécanique,
Cauchy, Augustin, pp. 406-412.
You can read some books about the history of physics for a general acquaintance with the authors and the published works from the previous centuries, but you must remain skeptical about any opinions presented there until you read yourself the primary works to verify if they really contain what is claimed about them, or they contain something else.
I have found the reading of many old scientific papers, especially from the 19th century, surprisingly useful for a better understanding of the modern theories that I use now.
Even the original works written in English, like those of Hamilton, pose serious problems when you are not careful, because many words used in physics have changed in meaning during the time, some of them multiple times (e.g. "energy", "action" or "force"). Those who are not aware of this frequently reach wrong conclusions about who has said what.
A few authors have actually read the primary sources, but those typically do not understand physics so well as to be able to distinguish the important concepts from those of little importance, so they are not able to trace the evolution of the important concepts :-(
The only foolproof method to understand the history of physics is to read very carefully the original works (carefully, because the words and the notations used may be very different from those used now). Fortunately, that has become much easier now than before, because there are many online repositories with digitized scientific works from the previous centuries.
For example, "Sir William Rowan Hamilton (1805-1865): Mathematical Papers":
https://www.emis.de/classics/Hamilton/index.html
The most important for this thread are (especially the 2nd, which introduces the modern Lagrangian formulation): 1834-04: “On a General Method in Dynamics”, and 1834-10 (but published in 1835): “Second Essay on a General Method in Dynamics”.
The first who has shown how to rewrite the second order system of Lagrange equations into the first order system of equations now called Hamilton's equations (i.e. by using the equivalent of the Legendre transformation) was Poisson in 1809, but the last time when I have searched for that work online I could not find it.
After Poisson, Cauchy has presented in 1831 a method equivalent with that published by Hamilton in 1835. I also could not find online the 1831 work, but an extract of it has been republished in 1837 and this can be found online in many places, for instance at:
http://www.numdam.org/volume/JMPA_1837_1_2_/
Note sur la variation des constantes arbitraires dans les problèmes de Mécanique, Cauchy, Augustin, pp. 406-412.
You can read some books about the history of physics for a general acquaintance with the authors and the published works from the previous centuries, but you must remain skeptical about any opinions presented there until you read yourself the primary works to verify if they really contain what is claimed about them, or they contain something else.
I have found the reading of many old scientific papers, especially from the 19th century, surprisingly useful for a better understanding of the modern theories that I use now.