This thesis studies ground resonance, a critical rotorcraft instability. The linearized equations of motion contain periodic coefficients, necessitating dedicated stability analysis methods. Usually, they are unfit for the introduction of non-linear elements and the identification of Limit Cycle Oscillations. Two procedures, proposed in past studies, are presented: the Floquet method for Linear Time Periodic systems, and the LTI Harmonic Decomposition. The latter produces a LTI system, which is compatible with non-linear analyses. An in-depth overview is provided of the derivation of the two methods, their stability criteria, their relationship, and a procedure to assess the harmonic composition of all modes. The procedures are applied to Hammond's rotor, the simplest ground resonance model, with various damper configurations, different number of inactive dampers, and different number of blades. The two methods provide close results in all cases, thus proving their equivalence and their interchangeability. Moreover, they provide new insight into the relationship between the model, stability and harmonics. A criterion for proper application of the LTI harmonic decomposition is formulated and tested. The LTI harmonic decomposition of the rotor with one inactive damper is used to build a quasi-linearized system through a Describing Function approach. The missing damper is reintroduced as a non-linear element, with variable free-play. Limit Cycle Oscillations are found and analyzed. These findings show how LTI harmonic decomposition is suitable for analyzing non-linear rotorcraft stability.