The ubiquitous Lagrangian

Analysis Seminar
Monday, August 25, 2008 - 4:00pm for 1 hour (actually 50 minutes)
Skiles 255
Maria Clara Nucci – Dept. of Mathematics and Informatics, University of Perugia
Jeff Geronimo
In any standard course of Analytical Mechanics students are indoctrinated that a Lagrangian have a profound physical meaning (kinetic energy minus potential energy) and that Lagrangians do not exist in the case of nonconservative system.  We present an old and regretfully forgotten method by Jacobi which allows to find many nonphysical Lagrangians of simple physical models (e.g., the harmonic oscillator) and also of nonconservative systems (e.g., the damped oscillator).  The same method can be applied to any equation of second-order, and extended to fourth-order equations as well as systems of second and first order. Examples from Physics, Number Theory and Biology will be provided.