Group theoretic methods for approximate invariants and Lagrangians for some classes of y″+εF(t)y′+y=f(y,y′)

摘要: Abstract Some recent results on the Lie symmetry generators of equations with a small parameter and relationship between symmetries conservation laws for such are used to construct first integrals Lagrangians autonomous weakly non-linear systems, y″+eF(t)y′+y=f (y,y′) . An adaptation theorem that provides point leave invariant functional involving Lagrangian is presented. A detailed example illustrate method given (and other examples discussed). The (approximate) generators, invariants maintain perturbation order ‘small parameter’ stipulated in equation — this case.