On Lagrangians with Reduced-Order Euler-Lagrange Equations

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2018
• Main Author: Saunders, D.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2018
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/209761
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On Lagrangians with Reduced-Order Euler-Lagrange Equations / D. Saunders // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 9 назв. — англ.

If a Lagrangian defining a variational problem has order k, then its Euler-Lagrange equations generically have order 2k. This paper considers the case where the Euler-Lagrange equations have order strictly less than 2k, and shows that in such a case the Lagrangian must be a polynomial in the highest...