Lie point symmetries and the time-independent integral of the damped harmonic oscillator

There has been growing interest recently in identifying the time-independent integral in dissipative systems. In this paper, we construct the time-independent integral for the damped harmonic oscillator from the time translational Lie vector field using the recently proposed λ-symmetries method (Muriel and Romero 2009 J. Phys. A: Math. Theor. 42 365207) and establish a group theoretical interpretation of the time-independent integral admitted by the damped harmonic oscillator. © 2011 The Royal Swedish Academy of Sciences.