Explicit motion of dynamic systems with position constraints |
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Authors: | Email author" target="_blank">Hee?Chang?EunEmail author Keun-Hyuk?Yang Heon-Soo?Chung |
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Affiliation: | (1) Department of Architectural Engineering, Cheju National University, Ara 1 Dong, 694-756 Jeju, Korea;(2) Department of Architectural Engineering, Chung-Ang University, Huksuk-Dong, Dongjak-Ku, 156-756 Seoul, Korea |
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Abstract: | Although many methodologies exist for determining the constrained equations of motion, most of these methods depend on numerical
approaches such as the Lagrange multiplier’s method expressed in differential/algebraic systems. In 1992, Udwadia and Kalaba
proposed explicit equations of motion for constrained systems based on Gauss’s principle and elementary linear algebra without
any multipliers or complicated intermediate processes. The generalized inverse method was the first work to present explicit
equations of motion for constrained systems. However, numerical integration results of the equation of motion gradually veer
away from the constraint equations with time. Thus, an objective of this study is to provide a numerical integration scheme,
which modifies the generalized inverse method to reduce the errors. The modified equations of motion for constrained systems
include the position constraints of index 3 systems and their first derivatives with respect to time in addition to their
second derivatives with respect to time. The effectiveness of the proposed method is illustrated by numerical examples. |
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Keywords: | Generalized Inverse Numerical Integration Numerical Error Position Constraint |
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