Abstract
Assuming that the existence of the constraints yields the change of the inertia force, this study derives the time-varying mass matrix for describing the constrained dynamic equation. It is displayed that the results corresponds with the ones by Udwadia and Kalaba. The numerical results obtained by integrating the constrained dynamic equation of second-order differential equations yield the errors in the satisfaction of the constraints. Modifying the derived dynamic equation this study presents a numerical algorithm to reduce the errors and to compute more precise motion. It is illustrated that the proposed method can be more precisely utilized in constrained mechanical systems through two applications of constrained nonlinear robotic systems.
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Recommended by Associate Editor Sungsoo Rhim
Salam Rahmatalla received his M.S. and Ph.D degrees in Civil and Environmental Engineering from The University of Iowa, Iowa City, IA, USA, in 2002 and 2004, respectively. Dr. Rahmatalla is currently an Assistant Professor at the Department of Civil and Environmental Engineering, The University of Iowa. Rahmatalla’a research interests include structural damage detection, dynamics and control of mechanical systems, and human biomechanics.
Eun-Taik Lee received his Ph.D. degree in Civil Engineering from SUNY/ Buffalo USA in 1992. Dr. Lee is currently the Professor at the School of Architecture & Building Science, College of Engineering, Chung-Ang University, Seoul, Korea. Dr. Lee’s research interests include structural remodeling, ubiquitous high-rise buildings, high-performance steel, performance-based structural design, and applied mechanics.
Hee-Chang Eun received his M.S. and Ph.D degrees in Civil Engineering from SUNY at Buffalo and USC, USA, in 1992 and 1995, respectively. Dr. Eun currently is a Professor at the Department of Architectural Engineering, Kangwon National University, Chuncheon, Korea. Dr. Eun’s research interests include structural damage detection, dynamics and control, and applied mechanics.
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Rahmatalla, S., Lee, ET. & Eun, HC. Numerical integration scheme to reduce the errors in the satisfaction of constrained dynamic equation. J Mech Sci Technol 27, 941–949 (2013). https://doi.org/10.1007/s12206-013-0205-9
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DOI: https://doi.org/10.1007/s12206-013-0205-9