New form of Kane's equations of motion for constrained systems

Journal of Guidance, Control, and Dynamics

Volumn 26, Issue 1, 2003, Pages 79-88

  Bajodah, Abdulrahman H ^a   Hodges, Dewey H ^b   Chen, Ye Hwa ^c  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b Georgia Institute of Technology   (United States)

^c GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONSTRAINT THEORY; CONTROL SYSTEM ANALYSIS; CONTROL SYSTEM SYNTHESIS; MATHEMATICAL MODELS; NONLINEAR CONTROL SYSTEMS;

CONSTRAINED SYSTEMS; NONHOLONOMIC SYSTEMS;

EQUATIONS OF MOTION;

EID: 0037269442     PISSN: 07315090     EISSN: 15333884     Source Type: Journal    
DOI: 10.2514/2.5017     Document Type: Article

References (48)

1. Kane, T. R., and Wang, C. F., "On the Derivation of Equations of Motion," Journal of the Society of Industrial and Applied Mathematics, Vol. 13, No. 2, 1965, pp. 487-492.
2. Kane, T. R., and Levinson, D. A., Dynamics: Theory and Applications, 1st ed., Series in Mechanical Engineering, McGraw-Hill New York, 1985.
3. Mitiguy, P. C., and Kane, T. R., "Motion Variables Leading to Efficient Equations of Motion," International Journal of Robotics Research, Vol. 15, No. 5, 1996, pp. 522-532.
4. Gibbs, J. W., "On the Fundamental Formulas of Dynamics," American Journal of Mathematics, Vol. 2, 1879, pp. 49-64.
5. Appell, P., "Sur les mouvements de roulment; équations du mouvement analougues à celles de Lagrange," Comptes Rendus, Vol. 129, 1899, pp. 317-320.
6. Desloge, E. A., "A Comparison of Kane's Equations of Motion and the Gibbs-Appell Equations of Motion," American Journal of Physics, Vol. 54, No. 5, 1986, pp. 470, 471.
7. Kane, T. R., "Rebuttal to 'A Comparison of Kane's Equations of Motion and the Gibbs-Appell Equations of Motion," American Journal of Physics, Vol. 54, No. 5, 1986, p. 472.
8. Desloge, E. A., "Relationship Between Kane's Equations and the Gibbs-Appell Equations," Journal of Guidance, Control, and Dynamics, Vol. 10, No. 1, 1987, pp. 120-122.
9. Levinson, D. A., "Comment on 'Relationship Between Kane's Equations and the Gibbs-Appell Equations,"' Journal of Guidance, Control, and Dynamics, Vol. 10, No. 6, 1987, p. 593.
10. Keat, J. E., "Comment on 'Relationship Between Kane's Equations and the Gibbs-Appell Equations,"' Journal of Guidance, Control, and Dynamics, Vol. 10, No. 6, 1987, pp. 594, 595.
11. Rosenthal, D. E., "Comment on 'Relationship Between Kane's Equations and the Gibbs-Appell Equations,"' Journal of Guidance, Control, and Dynamics, Vol. 10, No. 6, 1987, pp. 595, 596.
12. Banerjee, A. K., "Comment on 'Relationship between Kane's Equations and the Gibbs-Appell Equations,"' Journal of Guidance, Control, and Dynamics, Vol. 10, No. 6, 1987, pp. 596, 597.
13. Huston, R. L., "Comment on 'Relationship Between Kane's Equations and the Gibbs-Appell Equations,"' Journal of Guidance, Control, and Dynamics, Vol. 11, No. 2, 1988, p. 191.
14. Desloge, E. A., "The Gibbs-Appell Equations of Motion," American Journal of Physics, Vol. 56, No. 9, 1988, pp. 841-846.
15. Desloge, E. A., "Efficacy of the Gibbs-Appell Method for Generating Equations of Motion for Complex Systems," Journal of Guidance, Control, and Dynamics, Vol. 12, No. 1, 1989, pp. 114-116.
16. Sharf, I., D'eleuterio, G. M. T., and Hughes, P. C., "On the Dynamics of Gibbs, Appell, and Kane," European Journal of Mechanics. A, Solids, Vol. 11, No. 2, 1992, pp. 145-155.
17. Huston, R., "On the Equivalence of Kane's Equations and Gibbs' Equations for Multibody Dynamics Formulations," Mechanical Research Communications, Vol. 14, No. 2, 1987, pp. 123-131.
18. Lesser, M., "A Geometrical Interpretation of Kane's Equations," Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences, Vol. 436, No. 1896, 1992, pp. 69-87.
19. Kane, T. R., and Levinson, D. A., "Formulation of Equations of Motion for Complex Spacecraft," Journal of Guidance and Control, Vol. 3, No. 2, 1980, pp. 99-112.
20. Kane, T. R., and Levinson, D. A., "Use of Kane's Dynamical Equations in Robotics," International Journal of Robotics Research, Vol. 2, No. 3, 1983, pp. 3-21.
21. Kane, T. R., and Levinson, D. A., "Multibody Dynamics," Journal of Applied Mechanics, Vol. 50, No. 4b, 1983, pp. 1071-1078.
22. Rosenthal, D., and Sherman, M., "High Performance Multibody Simulations via Symbolic Equation Manipulation and Kane's Method," Journal of Astronautical Sciences, Vol. 34, No. 3, 1986, pp. 223-239.
23. Rosenthal, D., "An Order n Formulation for Robotic Systems," Journal of Astronautical Sciences, Vol. 38, No. 4, 1990, pp. 511-529.
24. Anderson, K., "Recursive Derivation of Explicit Equations of Motion for the Efficient Dynamic/Control Simulation of Large Multibody Systems," Ph.D. Dissertation, Dept. of Mechanical Engineering, Stanford Univ., Stanford, CA, 1990.
25. Anderson, K., "An Order-N Formulation for the Motion Simulation of General Multi-rigid-body Constrained Systems," Computers and Structures, Vol. 43, No. 3, 1992, pp. 565-579.
26. Anderson, K., "An Efficient Formulation for the Modeling of General Multi-flexible-body Constrained Systems," International Journal of Solids and Structures, Vol. 30, No. 7, 1993, pp. 921-945.
27. Anderson, K., "Efficient Modelling of Constrained Multibody Systems for Application with Parallel Computing," Zeitschrift Fur Angewandte Mathematik und Mechanik, Vol. 73, No. 6, 1993, pp. 935-939.
28. Lee, D., Hodges, D., and Patil, M., "Multi-Flexible-Body Dynamic Analysis of Horizontal-Axis Wind Turbines," Journal of Wind Energy (to be published).
29. Pars, L. A., A Treatise on Analytical Dynamics, Ox Bow, Woodridge, CT, 1979, pp. 41-44.
30. Gauss, C. F., "Über ein Neues Allgemeine Grundgesatz der Mechanik," Journal Für Die Reine Und Angewandte Mathematik, Vol. 4, 1829, pp. 232-235.
31. Wehage, R. A., and Haug, E. J., "Generalized Coordinate Partitioning for Dimension Reduction in Analysis of Constrained Dynamic Systems," Journal of Mechanical Design, Vol. 104, Jan. 1982, pp. 247-255.
32. Shabana, A. A., Dynamics of Multibody Systems, 2nd ed., Cambridge Univ. Press, Cambridge, England, U.K., 1998, pp. 251-254.
33. Wang, J. T., and Huston, R. L., "Kane's Equations With Undetermined Multipiers-Application to Constrained Multibody Systems," Journal of Applied Mechanics, Vol. 54, No. 2, 1987, pp. 424-429.
34. Huston, R., "Constraint Forces and Undetermined Multipliers in Constrained Multibody Systems," Multibody System Dynamics, Vol. 3, No. 4, 1999, pp. 381-389.
35. Su, C.-Y., Oya, M., and Katoh, R., "Robust Adaptive Motion/Force Control of Uncertain Nonholonomic Mechanical Systems," Proceedings of the American Control Conference, American Automatic Control Council, Evanston, IL, 2001, pp. 3268-3273.
36. Gofron, M., and Shabana, A., "Control Structure Interaction in the Nonlinear Analysis of Flexible Mechanical Systems," Nonlinear Dynamics, Vol. 4, No. 2, 1993, pp. 183-206.
37. Gofron, M., and Shabana, A., "Effect of the Deformation in the Inertia Forces on the Inverse Dynamics of Planar Flexible Mechanical Systems," Nonlinear Dynamics, Vol. 6, No. 1, 1994, pp. 1-20.
38. Agrawal, O., and Shabana, A., "Dynamic Analysis of Multibody Systems Using Component Modes," Computers and Structures, Vol. 21, No. 6, 1985, pp. 1303-1312.
39. Yoo, W., and Haug, E., "Dynamics of Flexible Mechanical Systems Using Vibration and Static Correction Modes," Journal of Mechanisms, Transmissions, and Automation in Design, Vol. 108, Sept. 1986, pp. 315-322.
40. Bauchau, O., and Rodriguez, J., "Modeling of Joints with Clearance in Flexible Multibody Systems," International Journal of Solids and Structures, Vol. 39, No. 1, 2002, pp. 41-63.
41. Udwadia, F. E., and Kalaba, R. E., "A New Perspective on Constrained Motion," Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences, Vol. 439, No. 1906, 1992, pp. 407-410.
42. Udwadia, F. E., and Kalaba, R. E., "On Motion," Journal of the Franklin Institute, Vol. 330, No. 3, 1993, pp. 571-577.
43. Chen, Y. H., "Second-Order Constriants for Equations of Motion of Constrained Systems," IEEE/ASME Transactions on Mechatronics, Vol. 3, No. 3, 1998, pp. 240-248.
44. Udwadia, F. E., and Kalaba, R. E., "The Geometry of Constrained Motion," Zeitschrift Fur Angewandte Mathematik und Mechanik, Vol. 75, No. 8, 1995, pp. 637-640.
45. Udwadia, F. E., "Equations of Motion For Mechanical Systems: A Unified Approach," International Journal of Non-Linear Mechanics, Vol. 31, No. 6, 1996, pp. 951-958.
46. Itiki, C., Kalaba, R. E., and Udwadia, F. E., "Inequality Constraints in the Process of Jumping," Journal of Applied Mathematics and Computation, Vol. 78, Nos. 2/3, 1996, pp. 163-173.
47. Chen, Y. H., "Equations of Motion of Constrained Mechanical Systems: Given Force Depends on Constraint Force," Mechatronics, Vol. 9, No. 4, 1999, pp. 411-428.
48. Chen, Y. J., "Pars's Acceleration Paradox," Journal of the Franklin Institute, Vol. 335B, No. 5, 1998, pp. 871-875.