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# Tenenbaum

# 12, December 2015
УДК: 629.785
The Mathematical Model of Thread Unrolling from a Bobbin
Engineering Education # 05, May 2014
DOI: 10.7463/0514.0704634
The paper describes a mathematical model for simulating a flexible thread unrolling from a bobbin. The real kinematics of unrolling is considered, but the problem of contact between the thread and bobbin is avoided. This results in great reduction of model «stiffness». The model has a constant dimension thereby simplifying the algorithm. The feature of this model is that there is no need to have many nodes on one thread turn to ensure stability and convergence. This model is tested by the simplified problem of Heliogyro solar sail deploying. From simulation results it is clear that a transversal motion of solar sail is almost independent on simulation model parameters, i.e. the model convergence.
Engineering Education # 12, December 2012
DOI: 10.7463/1212.0493439
While deploying a rotary solar sail it may be necessary to increase its angular velocity (that is, to make its additional deployment). To achieve this, an additional torque is required (additional deployment torque). Due to fragility of the frameless structure it can lead to considerable displacements of the solar sail wings relative to the stiff part of the spacecraft, even to reeling the wings up on the spacecraft. In this paper the authors propose a mathematical model with two degrees of freedom for estimating the dynamic of the spacecraft with two-blade rotary solar sail with an external torque moment. The model is based on the nonlinear motion equations of two-element pendulum (the first pendulum simulates the stiff part of the spacecraft; second pendulum simulates the blades of the solar sail). This model allows to estimate an admissible torque considering the restriction on the deviation angle of the blades from the stationary position. Software for calculations was developed; dependence of additional deployment on the system parameters and character of the load (suddenness) was analyzed.

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