A variational principle motivated by the optimal rod theory

Abstract

In this work we show that a number of well known nonlinear second order ODE appearing in theoretical physics provide the necessary condition for the minimum of the functional I = ∫ab L(x, ẍ, t) dt with the Lagrangian L = (-λF(t) x/ẍ)α. Also we prove that those second-order differential equations may be viewied as conservation laws for the corresponding Euler-Lagrange equations that are the fourthorder ODE. Several special cases that have importance in physics, mechanics and optimal rod theory are studied in detail. © Springer-Verlag 2000.