Equations of motion for constrained multibody systems and their control

Journal of Optimization Theory and Applications

Volumn 127, Issue 3, 2005, Pages 627-638

  Udwadia, F E ^a  

^a University of Southern California ^*  (United States)

Author keywords

Analytical dynamics; Constrained motion; Exact control of nonlinear systems; Explicit equations of motion; Multibody and nonlinear systems

Indexed keywords

NONLINEAR EQUATIONS; NONLINEAR SYSTEMS;

ANALYTICAL DYNAMICS; CONSTRAINED MOTION; CONTROL OF NONLINEAR SYSTEM; EQUATION OF MOTION; EXACT CONTROL OF NONLINEAR SYSTEM; EXACT CONTROLS; EXPLICIT EQUATION OF MOTION; EXPLICIT EQUATIONS; MULTI-BODY; MULTIBODY AND NONLINEAR SYSTEM;

EQUATIONS OF MOTION;

EID: 29144469347     PISSN: 00223239     EISSN: 15732878     Source Type: Journal    
DOI: 10.1007/s10957-005-7507-8     Document Type: Article

References (15)

1. LAGRANGE, J. L., Mechanique Analytique, Mme Ve Coureier, Paris, France, 1811.
2. GIBBS, J. W., On the Fundamental Formulae of Dynamics, American Journal of Mathematics, Vol. 2, pp. 49-64, 1879.
3. APPELL, P., Sur une Forme Generale des Equations de la Dynamique, Comptes Rendus Hebdomadaires des Seances de l'Academie des Sciences, Paris, Vol. 129, pp. 459-460, 1899.
4. POINCARE, H., Sur une Forme Nouvelle des Equations de la Mechanique, Comptes Rendus Hebdomadaires des Seances de l'Academie des Sciences, Paris, Vol. 132, pp. 369-371, 1901.
5. GAUSS, C. F., Uber Ein Neues Allgemeines Grundgsetz der Mechanik, Journal für die Reine und Angewandte Mathematik, Vol. 4, pp. 232-235, 1829.
6. DIRAC, P. A. M., Lectures in Quantum Mechanics, Yeshiva University, New York, NY, 1964.
7. UDWADIA, F. E., and KALABA, R. E., A New Perspective on Constrained Motion, Proceedings of the Royal Society of London, Vol. 439A, pp. 407-410, 1992.
8. CHETAEV, N. G., Theoretical Mechanics, Mir Publishers, Moscow, Russia, 1989.
9. SYNGE, J. L., On the Geometry of Dynamics, Philosophical Transactions of the Royal Society of London, Vol. 226A pp. 31-106, 1927.
10. UDWADIA, F. E., and KALABA, R. E., On the Foundations of Analytical Dynamics, International Journal of Nonlinear Mechanics, Vol. 37, pp. 1079-1090, 2002.
11. UDWADIA, F. E., and KALABA, R. E., What is the General Form of the Explicit Equations of Motion for Mechanical Systems?, Journal of Applied Mechanics, Vol. 39, pp. 335-339, 2002.
12. UDWADIA, F. E., and KALABA, R. E., Analytical Dynamics: A New Approach, Cambridge University Press, Cambridge, UK, 1996.
13. UDWADIA, F. E., KALABA, R. E., and HEE-CHANG, E., Equations of Motion for Constrained Mechanical Systems and the Extended D'Alembert Principle, Quarterly of Applied Mathematics, Vol. 56, 321-331, 1997.
14. UDWADIA, F. E., A New Perspective on the Tracking Control of Nonlinear Structural and Mechanical Systems, Proceedings of the Royal Society of London, Vol. 459A, pp. 1783-1800, 2003.
15. UDWADIA, F. E., Exact Tracking Control for Nonlinear Structural and Mechanical Systems, Proceedings of the International Congress on Applied and Theoretical Mechanics, Warsaw, Poland, August 15-21, 2004.