On the Origins of Hamilton’s Principle(s)

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this work authors show an overview of the historical, cultural and epistemological back ground that is key for Hamilton’s positions on mechanics. After, Authors shows some of Hamilton’s original papers to highlight how he posed his principle(s) on the wake of his forerunners and how his principles are linked with the search of a unitary view for physics. After careful reading, I consider that the work is well presented and could be reconsidered for publication after following revisions:

1) The originality of this work must be more discussed in the end of introduction.

2) The text should be checked for some minor typical errors.

3) Some equations must be referenced for example Eq (1), (2), (3), (4), and (5).

4) In the conclusion the author must give the conclusions point by point.

5) The manuscript does not contain references from the past 3 to 5 years. I encourage authors to added the recent references as:

DOI : https://doi.org/10.1016/j.compstruct.2021.114028

DOI : https://doi.org/10.1007/s10483-011-1470-9

DOI : 10.3934/jgm.2021002

DOI : https://doi.org/10.1007/s11012-004-2198-z

 

Comments on the Quality of English Language

The article is well written by the authors. There are few errors in English of this work.

Author Response

Dear Reviewer, thanks for your reading and precious comments.

Some typos are corrected and some changes are made to improve the text.

 We have numbered all the equations apart those appearing in quotations.

We divided the conclusions into paragraphs to make them clearer.

We added  new references, some of them are very recent.

Reviewer 2 Report

Comments and Suggestions for Authors

The article gives a deep analysis of the history of Hamilton's principle and a detailed exposition of Hamilton's works. Everything that I knew about this before I found confirmation in this work, and learned a lot of new and interesting things. The article is well written, contains many important references and certainly deserves publication. I have no comments on the essence of the work, I just want to draw the authors' attention to two works concerning this topic, maybe the authors will find it useful to add them to the list of references:
Arnold, V. I. 1989. Mathematical methods of classical mechanics. New
York: Springer-Verlag.
Levin, M. L. 1978. How light conquers darkness (W. R. Hamilton and the
concept of group velocity). Sov. Phys. Uspekhy. 21:639–40.

However, am not sure that this nice text can be called concise.

Author Response

Dear Reviewer, thanks for your reading and precious comments.

We added the papers you suggested.

Reviewer 3 Report

Comments and Suggestions for Authors

This article reviews the historic perspective of Hamilton's principle. It connects the pre-Hamilton era and the post-Hamilton era, and shows the motivation and idea of Hamilton's principle. 

This is a well-written, concise, and inspiring article. I strongly recommend the publication of this article. 

Author Response

Dear Reviewer, thanks for your reading and precious comments.