To understand the main orographic and non-orographic sources of gravity waves (GWs) over South America during an Experiment (Rapp et al, 2021, https://doi.org/10.1175/BAMS-D-20-0034.1), we propose the application of a rotational spectral analysis based on methods originally developed for oceanographic studies. This approach is deployed in a complex scenario of large-amplitude GWs by applying it to reanalysis data. We divide the atmospheric region of interest into two height intervals. The simulations are compared with lidar measurements during one of the flights. From the degree of polarization and the total energy of the GWs, the contribution of the upward and downward wave packets is described as a function of their vertical wavenumbers. At low levels, a larger downward energy flux is observed in a few significant harmonics, suggesting inertial GWs radiated at polar night jet levels, and below, near to a cold front. In contrast, the upward GW energy flux, per unit area, is larger than the downward flux, as expected over mountainous areas. The main sub-regions of upward GW energy flux are located above Patagonia, the Antarctic Peninsula and only some oceanic sectors. Above the sea, there are alternating sub-regions dominated by linearly polarized GWs and sectors of downward GWs. At the upper levels, the total available GW energy per unit mass is higher than at the lower levels. Regions with different degrees of polarization are distributed in elongated bands. A satisfactory comparison is made with an analysis based on the phase difference between temperature and vertical wind disturbances.