On the Origins of Hamilton’s Principle(s)
This entry first provides an overview of the historical, cultural and epistemological background that is key for Hamilton’s positions on mechanics. We consider the investigations on geometrical optics in the 17th and 18th centuries, Euler’s and Lagrange’s foundations of variational calculus in the 1...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-09-01
|
| Series: | Encyclopedia |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2673-8392/4/4/94 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1846104901320441856 |
|---|---|
| author | Paolo Bussotti Danilo Capecchi Giuseppe Ruta |
| author_facet | Paolo Bussotti Danilo Capecchi Giuseppe Ruta |
| author_sort | Paolo Bussotti |
| collection | DOAJ |
| description | This entry first provides an overview of the historical, cultural and epistemological background that is key for Hamilton’s positions on mechanics. We consider the investigations on geometrical optics in the 17th and 18th centuries, Euler’s and Lagrange’s foundations of variational calculus in the 18th century to find extrema of physical quantities expressed as infinite sums of infinitesimals (today, we would say ‘definite integrals’), and Lagrange’s introduction of a revolutionary analytical mechanics, all of which are all fertile grounds for Hamilton’s steps—first, in what we could call analytical optics, then in an advanced form of analytical mechanics. Having provided such an overview, we run through some of Hamilton’s original papers to highlight how he posed his principle(s) in the wake of his forerunners and how his principles are linked with the search for a unitary view of physics. |
| format | Article |
| id | doaj-art-12df968fd6184f6c85729d320d4565eb |
| institution | Kabale University |
| issn | 2673-8392 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Encyclopedia |
| spelling | doaj-art-12df968fd6184f6c85729d320d4565eb2024-12-27T14:22:58ZengMDPI AGEncyclopedia2673-83922024-09-01441454147110.3390/encyclopedia4040094On the Origins of Hamilton’s Principle(s)Paolo Bussotti0Danilo Capecchi1Giuseppe Ruta2Dipartimento di Studi Umanistici e del Patrimonio Culturale, Università di Udine, 33100 Udine, ItalySISFA, Società Italiana Storici Fisica e Astronomia, 80125 Naples, ItalyDipartimento di Ingegneria Strutturale e Geotecnica, Università di Roma “La Sapienza”, 00184 Rome, ItalyThis entry first provides an overview of the historical, cultural and epistemological background that is key for Hamilton’s positions on mechanics. We consider the investigations on geometrical optics in the 17th and 18th centuries, Euler’s and Lagrange’s foundations of variational calculus in the 18th century to find extrema of physical quantities expressed as infinite sums of infinitesimals (today, we would say ‘definite integrals’), and Lagrange’s introduction of a revolutionary analytical mechanics, all of which are all fertile grounds for Hamilton’s steps—first, in what we could call analytical optics, then in an advanced form of analytical mechanics. Having provided such an overview, we run through some of Hamilton’s original papers to highlight how he posed his principle(s) in the wake of his forerunners and how his principles are linked with the search for a unitary view of physics.https://www.mdpi.com/2673-8392/4/4/94Hamilton’s principle(s)analytical mechanicsstationary actionleast actionvarying action |
| spellingShingle | Paolo Bussotti Danilo Capecchi Giuseppe Ruta On the Origins of Hamilton’s Principle(s) Encyclopedia Hamilton’s principle(s) analytical mechanics stationary action least action varying action |
| title | On the Origins of Hamilton’s Principle(s) |
| title_full | On the Origins of Hamilton’s Principle(s) |
| title_fullStr | On the Origins of Hamilton’s Principle(s) |
| title_full_unstemmed | On the Origins of Hamilton’s Principle(s) |
| title_short | On the Origins of Hamilton’s Principle(s) |
| title_sort | on the origins of hamilton s principle s |
| topic | Hamilton’s principle(s) analytical mechanics stationary action least action varying action |
| url | https://www.mdpi.com/2673-8392/4/4/94 |
| work_keys_str_mv | AT paolobussotti ontheoriginsofhamiltonsprinciples AT danilocapecchi ontheoriginsofhamiltonsprinciples AT giusepperuta ontheoriginsofhamiltonsprinciples |