Abstract: This paper presents the nonlinear time-optimal controlfor the three-dimensional deployment process of a tethered subsatellitemodel, which also takes tether elasticity and the mission-relatedstate-control constraints into consideration. Instead of the commonly usedstate-space model, a second-order differential inclusion formulation isexploited in this work to achieve a significant reduction of the number ofsystem variables. The optimal control is solved by discretizing the optimalcontrol problem based on a direct algorithm, and numerically solving theresulting large-scale optimization problem via an NLP (nonlinearprogramming) solver. The case studies in the paper well demonstrate theperformance of the proposed strategy.