In large dynamical systems subjected to noise or forced oscillations, disturbances constantly arise over time. In this case, the small-signal stability is determined by the energy of perturbations accumulated in the system. To analyze this perturbation energy, this study proposes a novel physically motivated Lyapunov modal analysis (LMA) framework that combines selective modal analysis with the spectral decompositions of specially chosen Lyapunov functions. Based on this approach, we propose new modal indicators that characterize individual modes and modal interactions in connection with specific state variables. Conventional participation factors characterize the relative contributions of the system modes to the evolution of states. In contrast, the proposed Lyapunov participation factors make similar contributions to the Lyapunov functions that estimate the integral energy associated with the states and signals on an infinite or finite time interval. The Lyapunov modal interaction factors characterize the pairwise interaction between modes in terms of their mutual actions produced in states over time. We prove that the proposed modal indicators characterize the stability of individual modes and resonant modal interactions in linear parameter-varying systems and demonstrate the application of these indicators for the small-signal stability analysis of a two-area power system model. New indicators can be calculated independently for a selected part of the system spectrum and used to quickly assess the behavior of critical modes in large-scale dynamical systems.