The stellar dynamics of virialised systems is analysed within the search of undamped oscillations. In the case of a time-dependent Hamiltonian qualified after a generic Terzic'-Kandrup potential, the Emrakov-Lewis-Leach invariant is specified; as a result, an infinite set of conservation laws defining constants of motion is demonstrated to be obtained. Two methodologies are applied: the small-time parameter series expansion, and the slowly-varying higher-orders expansion. The results are apt to be applied to the case of the Emrakov-Lewis invariant, of the Emrakov-Lewis adiabatic invariant, and of the generalised Guenther-Leach generalised invariant. The verification of the series-expansion infinitesimal parameter is envisaged. WKB calculations are studied to be feasible.