Partial Noether operators and first integrals via partial Lagrangians

摘要

The notions of partial Lagrangians, partial Noether operators and partial Euler-Lagrange equations are used in the construction of first integrals for ordinary differential equations that need riot be derivable from variational principle; We obtain a Noether-like theorem that provides the first integral by means of a formula which ha the same structure as the Noether integral, However, the invariatice condition for the determination of the partial Noether operators is different as we have a partial Lagrangian and as a result partial Euler-Lagrange equations. Applications given include those that admit a standard Lagrangian such as the harmonic oscillator, modified Emden and Ermakov-Pinney equations and systems of two second-order equations that do not have standard Lagrangians. Copyright (c) 2007 John Wiley & Sons, Ltd.