Abstract
It is shown that given a Lagrangian for a system with a finite number of degrees of freedom, the existence of a variational symmetry is equivalent to the existence of coordinates in the extended configuration space such that one of the coordinates is ignorable. The proof given here, which only requires multivariable calculus, provides an elementary derivation of the partial differential equation that determines the variational symmetries of a given Lagrangian, which is obtained in treatises on the Lie theory of symmetries of differential equations or of variational calculus.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
