TY - JOUR
T1 - Construction of unwinding equation of motion for thin cable in spherical coordinate system
AU - Kim, Kun Woo
AU - Lee, Jae Wook
AU - Jang, Jin Seok
AU - Oh, Joo Young
AU - Kang, Ji Heon
AU - Kim, Hyung Ryul
AU - Yoo, Wan Suk
N1 - Publisher Copyright:
© IMechE 2017.
PY - 2018/4/1
Y1 - 2018/4/1
N2 - The transient-state unwinding equation of motion for a thin cable can be derived by using Hamilton’s principle for an open system, which can consider the mass change produced by the unwinding velocity in a control volume. In general, most engineering problems can be analyzed in Cartesian, cylindrical, and spherical coordinate systems. In the field of unwinding dynamics, until now, only Cartesian and cylindrical coordinate systems have been used. A spherical coordinate system has not been used because of the complexity of derivatives. Therefore, in this study, the unwinding motion of a thin cable was analyzed using a spherical coordinate system in both water and air, and the results were compared with the results in Cartesian and cylindrical coordinate systems. The unwinding motions in the spherical, Cartesian, and cylindrical coordinate systems were nearly same in both water and air. The error related to the total length was within 0.5% in water, and the error related to the maximum balloon radius was also within 0.5 % in air. Therefore, it can be concluded that it is possible to solve the transient-state unwinding equation of motion in a spherical coordinate system.
AB - The transient-state unwinding equation of motion for a thin cable can be derived by using Hamilton’s principle for an open system, which can consider the mass change produced by the unwinding velocity in a control volume. In general, most engineering problems can be analyzed in Cartesian, cylindrical, and spherical coordinate systems. In the field of unwinding dynamics, until now, only Cartesian and cylindrical coordinate systems have been used. A spherical coordinate system has not been used because of the complexity of derivatives. Therefore, in this study, the unwinding motion of a thin cable was analyzed using a spherical coordinate system in both water and air, and the results were compared with the results in Cartesian and cylindrical coordinate systems. The unwinding motions in the spherical, Cartesian, and cylindrical coordinate systems were nearly same in both water and air. The error related to the total length was within 0.5% in water, and the error related to the maximum balloon radius was also within 0.5 % in air. Therefore, it can be concluded that it is possible to solve the transient-state unwinding equation of motion in a spherical coordinate system.
KW - Cartesian and cylindrical coordinate systems
KW - spherical coordinate system
KW - thin cable
KW - transient-state unwinding equation of motion
KW - Unwinding dynamics
UR - http://www.scopus.com/inward/record.url?scp=85045447574&partnerID=8YFLogxK
U2 - 10.1177/0954406217705406
DO - 10.1177/0954406217705406
M3 - Article
AN - SCOPUS:85045447574
SN - 0954-4062
VL - 232
SP - 1208
EP - 1220
JO - Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science
JF - Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science
IS - 7
ER -