Euler's original derivation of elastica equation
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912323476652032 |
|---|---|
| author | Matsutani, Shigeki |
| author_facet | Matsutani, Shigeki |
| contents | Euler derived the differential equations of elastica by the variational method in 1744, but his original derivation has never been properly interpreted or explained in terms of modern mathematics. We elaborate Euler's original derivation of elastica and show that Euler used Noether's theorem concerning the translational symmetry of elastica, although Noether published her theorem in 1918. It is also shown that his equation is essentially the static modified KdV equation which is obtained by the isometric and isoenergy conditions, known as the Goldstein-Petrich scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09227 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Euler's original derivation of elastica equation Matsutani, Shigeki Mathematical Physics Differential Geometry Exactly Solvable and Integrable Systems Euler derived the differential equations of elastica by the variational method in 1744, but his original derivation has never been properly interpreted or explained in terms of modern mathematics. We elaborate Euler's original derivation of elastica and show that Euler used Noether's theorem concerning the translational symmetry of elastica, although Noether published her theorem in 1918. It is also shown that his equation is essentially the static modified KdV equation which is obtained by the isometric and isoenergy conditions, known as the Goldstein-Petrich scheme. |
| title | Euler's original derivation of elastica equation |
| topic | Mathematical Physics Differential Geometry Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2411.09227 |