Form invariances and Lutzky conserved quantities for Lagrange systems

This paper focuses on studying a form invariance which can result in a Lutzky conserved quantity for a Lagrange system. The criterion of the form invariance for the system is given. The necessary and sufficient condition under which the form invariance is a Lie symmetry for the system is obtained. Lutzky's result is utilized to prove that the form invariance can lead to a Lutzky conserved quantity. Two examples are finally given to illustrate the application of the result.