|Abstract Stratosphere high altitude tethered balloon (HATB) is a typical under-damping autonomous system, so it is required for the platform itself to be stable. However, it is hardly to investigate the platform stability theoretically through the classical Lyapunov first method, because there exist zero eigenvalues in the linearized model. The rigid translation and rotation equations with respect to any arbitrary point were presented, and then the general coordinate-based, second order, nonlinear dynamic model was proposed for HATB. In view of the limitation of the Lyapunov method, Lagrange theorem was applied to prove the platform stability problem from the perspective of energy. Numerical simulations demonstrate the coincidence with the theoretical analysis.