In this paper, we derive analytical closed-form expressions for time-varying generator participation factors that are valid throughout the post-contingency transient period. Combining these with conventional injection shift factors (ISFs) computed at the pre-disturbance steady-state operating point, post-contingency dynamic transmission-line flows after the outage of any one particular asset, such as a generator or load, can be accurately predicted. This is advantageous over conventional ISF-based contingency analysis, which is applicable only for the post-disturbance steady-state operating point. As such, operators can determine whether or not any transmission lines exceed their operational limits during the transient without repeated time-domain simulations for each credible contingency. We validate the proposed methodology via numerical case studies conducted on standard IEEE test systems.