Journal of Mechanical Science and Technology

  • 제17권4호
  • /
  • Pages.538-544
  • /
  • 2003
  • /
  • 1738-494X(pISSN)
  • /
  • 1976-3824(eISSN)
대한기계학회 (The Korean Society of Mechanical Engineers)
권호 표지

Explicit Motion of Dynamic Systems with Position Constraints

  • Eun, Hee-Chang (Department of Architectural Engineering, Cheju National University) ;
  • Yang, Keun-Hyuk (Department of Architectural Engineering, Chung-Ang University) ;
  • Chung, Heon-Soo (Department of Architectural Engineering, Chung-Ang University)
  • 발행 : 2003.04.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

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.

키워드

참고문헌

  1. Appell, P., 1911, 'Example De Mouvement D'un Point Assujetti A Une Liaison ExprimeePar Une Relation Non Lineaire Entre Les Composantes DeLa Vitesse,' Rend. Circ. Matem. Palermo., 32, pp. 48-50 https://doi.org/10.1007/BF03014784
  2. Baumgarte, J. W., 1972, 'Stabilization of Constraints and Integrals of Motion in Dynamical Systems,' Comp. Meth. in Appl. Mech. and Engineering, 1, pp. 1-16 https://doi.org/10.1016/0045-7825(72)90018-7
  3. Gear, C. W. and Petzold, L. R., 1984, 'ODE Methods for The Solution of Differential/Algebraic Systems,' SIAM J. Numer. Anal., 21, pp. 716-728 https://doi.org/10.1137/0721048
  4. Gear, C. W., Leimkuhler B. and Gupta G. K., 1985, 'Automatic Integration of Euler-Lagrange Equations with Constraints,' J. Comput. Appl. Math., 12 & 13, pp. 77-90 https://doi.org/10.1016/0377-0427(85)90008-1
  5. Gear, C. W., 1986, 'Maintaining Solution Invariants in The Numerical Solution of ODEs,' SIAM J. Sci. Stat. Comput., 7, pp. 734-743 https://doi.org/10.1137/0907050
  6. Gear, C. W., 1988, 'Differential-Algebraic Equation Index Transformations,' SIAM J. Sci. Stat. Comput., 9, pp. 39-47 https://doi.org/10.1137/0909004
  7. Gibbs, J. W., 1879, 'On the Fundamental Formulae of Dynamics,' American Journal of Mathematics, 2, pp. 49-64 https://doi.org/10.2307/2369196
  8. Kane, T. R., 1983, 'Formulation of Dynamical Equations of Motion,' Am. J. Phys. 51, pp. 974-977 https://doi.org/10.1119/1.13452
  9. Park, J. H., Yoo, H. H. and Hwang, Y., 2000, 'Computational Method for Dynamic Analysis of Constrained Mechanical Systems Using Partial Velocity Matrix Transformation,' KSME International Journal, Vol. 14, No. 2, pp. 159-167
  10. Park, J. H., Yoo, H. H., Hwang, Y. and Bae, D. S., 1997, 'Dynamic Analysis of Constrained Multibody Systems Using Kane's Method,' Transaction of the KSME, Vol. 21, No. 12, pp. 2156-2164
  11. Passerello, C. E. and Huston, R. L., 1973, 'Another Look at Nonholonomic Systems,' ASME Journal of Applied Mechanics, pp. 101-104
  12. Udwadia, F. E. and Kalaba, R. E., 1992, 'A New Perspective on Constrained Motion,' Proceedings of the Royal Society of London, 439, pp. 407-410 https://doi.org/10.1098/rspa.1992.0158