The Soil Moisture Active-Passive (SMAP) satellite is the only satellite with a large deployable space eccentric rotating ring truss antenna clamped along a generatrix and rounding a parallel axis. However, the active radar of SMAP satellite stopped working within months of its launch. What are the reasons leading to so dramatic consequences? It is a possibility that the satellite damage is caused by vibration. In this paper, the nonlinear breathing vibrations of the large deployable space eccentric rotating composite laminated ring truss antennas with the large radius are studied from a theoretical analysis of view. Referring to the equivalent model of the continuum circular cylindrical shell clamped along a generatrix, we propose a dynamic model of the eccentric rotating composite laminated circular cylindrical shell subjected to the lateral and the temperature excitations. Considering an eccentric rotating composite laminated circular cylindrical shell clamped along a generatrix and rounding a parallel axis, the nonlinear partial differential governing equations of motion are established by using Donnell thin shear deformation theory, von Karman-type nonlinear relation and Hamilton’s principle. The nonlinear ordinary differential governing equations of motion are obtained by using Galerkin discretization. Based on the theoretical model, the nonlinear breathing vibrations of the equivalent model are studied for the SMAP satellite antenna subjected to the lateral and the temperature excitations for the first time in this paper. Firstly, the effects of different parameters on the toggle condition of 1:2 internal resonance are studied. The effects of the radius and the eccentricity ratio on the natural frequencies are not obvious for the eccentric rotating composite laminated circular cylindrical shell. Furthermore, it is also found that the influence of the thickness and the eccentricity ratio on the resonant rotating speeds cannot be ignored for the eccentric rotating composite laminated circular cylindrical shell. Then, based on the case of 1:2 internal resonance and principal parametric resonance-1/2 subharmonic resonance, the parametric excitation T is selected as the controlling parameter to discover the nonlinear breathing vibrations of the eccentric rotating composite laminated circular cylindrical shell. The periodic and chaotic motions of the equivalent model for the SMAP satellite antenna are found when the rotating speed corresponds to the internal resonant point at the certain excitations for different lateral and temperature excitations. Therefore, the chaotic motions of the SMAP satellite antenna occur under the combined action of temperature parameter excitation and lateral excitation in the space environment. According to the research results of this paper, the active radar of the SMAP satellite may be damaged by severe nonlinear vibrations. We reasonably speculate that the failure of the active radar for the SMAP satellite antenna is caused by the nonlinear vibrations in 1:2 internal resonance. Thus, this paper not only provides a possible analysis for the failure of the SMAP satellite, but also provides the theoretical guidance for study of similar ring truss antennas. This research has important theoretical significance and engineering value.