Journal
NONLINEAR DYNAMICS
Volume 80, Issue 3, Pages 1565-1583Publisher
SPRINGER
DOI: 10.1007/s11071-015-1963-y
Keywords
Unwinding dynamics; Thin cable; Transient- and steady-state unwinding equations of motion
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Funding
- Agency for Defense Development (ADD)
- National Research Foundation of Korea [21A20131711119] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
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When a thin cable is unwound from a spool dispenser, factors that influence balloon shapes are initial tensile force, unwinding velocity, balloon height, package radius, and fluid condition. Historically, a thin cable's unwinding motion has been analyzed using transient- and steady-state unwinding equations of motion. The transient-state unwinding equation of motion can be derived by using Hamilton's principle for an open system in which mass can change within a control volume. In the process of solving the transient-state unwinding equation of motion, two-point boundary conditions are exactly adopted for each time step. The steady-state unwinding equation of motion can be derived by using a perturbation scheme from the transient-state unwinding equation of motion. To find a solution for the steady-state unwinding equation of motion, the shooting method is utilized, but due to insufficient boundary conditions at the lift-off point, finding a unique solution is impossible. Therefore, analysis of the unwinding motion of a thin cable should be performed using the transient-state unwinding equation of motion.
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