The objective of this paper is to study the dynamic modeling and simulation of a tether-net/gripper system during an impact, while it is being deployed or retrieved by a winch on a satellite orbiting around earth. We stick to Tether-Net system but the analysis is applicable to Tether-Gripper systems too. We assume that the net is deployed from the satellite in orbit and the motion is restricted to the orbital plane. This net captures a second satellite and tows it. The motion of a tether-net system can be broken down into the following phases: (i) Phase 1: Net is shot out from the satellite with the tether completely slack, (ii) Phase 2: Net comes to a location where the tether is taut while the drum on the orbiter is locked, (iii) Phase 3: Drum is unlocked and the net moves with the tether, (iv) Phase 4: Net captures a body. The continua (tether) is modeled using mode functions and coordinates. The theory of impulse and momentum can be used to model Phases 1, 2, and 4 of motion of the tether-net system. The dynamics of the motion of the system in phase 3 is characterized by differential and algebraic equations (DAEs). Matlab ODE solvers were used to solve these DAEs.

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