Prognostics of a nuclear system have been of interest, as it can dramatically reduce the operation and maintenance (O&M) cost. For the prognostics, degradation models for components in a nuclear system are needed. In this paper, we propose an online algorithm for discovery of hidden degradation dynamics of components in a nuclear system. The suggested algorithm has been built upon SINDy (Sparse Identification of the Non-linear Dynamics), an algorithm that discovers a set of equations of hidden nonlinear dynamics from a time series data of the states of a component. In this study, we propose a recursive version of SINDy, which is capable of updating the discovered equation whenever new data are received from sensors of the component. We applied the suggested algorithm to centrifugal pump operation data synthesized from a simplistic pump model to validate whether the suggested algorithm can discover hidden degradation dynamics. The results showed that the equations discovered by the recSINDy converged closer to the true equations as they were updated online over time. The recSINDy found the hidden degradation dynamics even with the existence of the 1.0% random noise in the data, although the time required to converge to the true equation was much longer and a few unnecessary terms are remained in the discovered equations.