Perturbation to Lie Symmetry and Lutzky Adiabatic Invariants for Lagrange Systems

Based on the concept of adiabatic invariant, perturbationto Lie symmetry and Lutzky adiabatic invariants for Lagrange systems arestudied by using different methods fromthose of previous works. Exactinvariants induced from Lie symmetry of the system without perturbation aregiven. Perturbation to Lie symmetry is discussed and Lutzky adiabaticinvariants of the system subject to perturbation are obtained.