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On general nonlinear constrained mechanical systems
1. | Aerospace and Mechanical Engineering, Civil Engineering, Mathematics, and Information and Operations Management, University of Southern California, Los Angeles, CA 90089-1453, United States |
2. | Department of Mechanical Engineering, Mahidol University, 25/25 Puttamonthon, Nakorn Pathom 73170, Thailand |
References:
[1] |
P. Appell, Sur une forme generale des equations de la dynamique, C. R. Acad. Sci. III, 129 (1899), 459-460. |
[2] |
P. Appell, Example de mouvement d'un point assujeti a une liason exprimee par une relation non lineaire entre les composantes de la vitesse, Rend. Circ. Mat. Palermo, 32 (1911), 48-50.
doi: 10.1007/BF03014784. |
[3] |
N. G. Chataev, "Theoretical Mechanics," Mir Publications, Moscow, 1989. |
[4] |
C. T. Chen, "Linear System Theory and Design," Oxford University Press, New York, 1999. |
[5] |
P. A. M. Dirac, "Lectures in Quantum Mechanics," New York, Yeshiva University Press, 1964. |
[6] |
C. Gauss, Uber ein neues allgemeines grundgesetz der mechanik, J. Reine Angew. Math., 4 (1829), 232-235.
doi: 10.1515/crll.1829.4.232. |
[7] |
W. Gibbs, On the fundamental formulae of dynamics, Am. J. Math., 2 (1879), 49-64.
doi: 10.2307/2369196. |
[8] |
H. Goldstein, "Classical Mechanics," Addison-Wesley, Reading, MA, 1981. |
[9] |
F. Graybill, "Matrices with Applications in Statistics," Wadsworth and Brooks, 1983. |
[10] |
G. Hamel, "Theoretische Mechanik: Eine Einheitliche Einfuhrung in die Gesamte Mechanik," Springer-Verlag, Berlin, New York, 1949. |
[11] |
J. L. Lagrange, "Mechanique Analytique," Paris: Mme Ve Courcier, 1787. |
[12] |
L. A. Pars, "A Treatise on Analytical Dynamics," Woodridge, CT: Oxbow Press, 1979. |
[13] |
R. Penrose, A generalized inverse of a matrices, Proc. Cambridge Philos. Soc., 51 (1955), 406-413.
doi: 10.1017/S0305004100030401. |
[14] |
A. Schutte and F. E. Udwadia, New approach to the modeling of complex multi-body dynamical systems, Journal of Applied Mechanics, 78 (2011), 11 pages.
doi: 10.1115/1.4002329. |
[15] |
E. C. G. Sudarshan and N. Mukunda, "Classical Dynamics: A Modern Perspective," Wiley, New York, 1974. |
[16] |
F. E. Udwadia and A. D. Schutte, Equations of motion for general constrained systems in Lagrangian mechanics, Acta Mechanica., 213 (2010), 111-129.
doi: 10.1007/s00707-009-0272-2. |
[17] |
F. E. Udwadia and P. Phohomsiri, Explicit equations of motion for constrained mechanical systems with singular mass matrices and applications to multi-body dynamics, Proceedings of the Royal Society of London A, 462 (2006), 2097-2117.
doi: 10.1098/rspa.2006.1662. |
[18] |
F. E. Udwadia and R. E. Kalaba, A new perspective on constrained motion, Proceedings of the Royal Society of London A, 439 (1992), 407-410.
doi: 10.1098/rspa.1992.0158. |
[19] |
F. E. Udwadia and R. E. Kalaba, An alternative proof for Greville's formula, Journal of Optimization Theory and Applications, 94 (1997), 23-28. |
[20] |
F. E. Udwadia and R. E. Kalaba, "Analytical Dynamics: A New Approach," Cambridge University Press, 1996.
doi: 10.1017/CBO9780511665479. |
[21] |
F. E. Udwadia and R. E. Kalaba, Explicit equations of motion for mechanical systems with non-ideal constraints, ASME J. Appl. Mech., 68 (2001), 462-467.
doi: 10.1115/1.1364492. |
[22] |
F. E. Udwadia and R. E. Kalaba, On the foundations of analytical dynamics, Int. J. Nonlin. Mech., 37 (2002), 1079-1090.
doi: 10.1016/S0020-7462(01)00033-6. |
show all references
References:
[1] |
P. Appell, Sur une forme generale des equations de la dynamique, C. R. Acad. Sci. III, 129 (1899), 459-460. |
[2] |
P. Appell, Example de mouvement d'un point assujeti a une liason exprimee par une relation non lineaire entre les composantes de la vitesse, Rend. Circ. Mat. Palermo, 32 (1911), 48-50.
doi: 10.1007/BF03014784. |
[3] |
N. G. Chataev, "Theoretical Mechanics," Mir Publications, Moscow, 1989. |
[4] |
C. T. Chen, "Linear System Theory and Design," Oxford University Press, New York, 1999. |
[5] |
P. A. M. Dirac, "Lectures in Quantum Mechanics," New York, Yeshiva University Press, 1964. |
[6] |
C. Gauss, Uber ein neues allgemeines grundgesetz der mechanik, J. Reine Angew. Math., 4 (1829), 232-235.
doi: 10.1515/crll.1829.4.232. |
[7] |
W. Gibbs, On the fundamental formulae of dynamics, Am. J. Math., 2 (1879), 49-64.
doi: 10.2307/2369196. |
[8] |
H. Goldstein, "Classical Mechanics," Addison-Wesley, Reading, MA, 1981. |
[9] |
F. Graybill, "Matrices with Applications in Statistics," Wadsworth and Brooks, 1983. |
[10] |
G. Hamel, "Theoretische Mechanik: Eine Einheitliche Einfuhrung in die Gesamte Mechanik," Springer-Verlag, Berlin, New York, 1949. |
[11] |
J. L. Lagrange, "Mechanique Analytique," Paris: Mme Ve Courcier, 1787. |
[12] |
L. A. Pars, "A Treatise on Analytical Dynamics," Woodridge, CT: Oxbow Press, 1979. |
[13] |
R. Penrose, A generalized inverse of a matrices, Proc. Cambridge Philos. Soc., 51 (1955), 406-413.
doi: 10.1017/S0305004100030401. |
[14] |
A. Schutte and F. E. Udwadia, New approach to the modeling of complex multi-body dynamical systems, Journal of Applied Mechanics, 78 (2011), 11 pages.
doi: 10.1115/1.4002329. |
[15] |
E. C. G. Sudarshan and N. Mukunda, "Classical Dynamics: A Modern Perspective," Wiley, New York, 1974. |
[16] |
F. E. Udwadia and A. D. Schutte, Equations of motion for general constrained systems in Lagrangian mechanics, Acta Mechanica., 213 (2010), 111-129.
doi: 10.1007/s00707-009-0272-2. |
[17] |
F. E. Udwadia and P. Phohomsiri, Explicit equations of motion for constrained mechanical systems with singular mass matrices and applications to multi-body dynamics, Proceedings of the Royal Society of London A, 462 (2006), 2097-2117.
doi: 10.1098/rspa.2006.1662. |
[18] |
F. E. Udwadia and R. E. Kalaba, A new perspective on constrained motion, Proceedings of the Royal Society of London A, 439 (1992), 407-410.
doi: 10.1098/rspa.1992.0158. |
[19] |
F. E. Udwadia and R. E. Kalaba, An alternative proof for Greville's formula, Journal of Optimization Theory and Applications, 94 (1997), 23-28. |
[20] |
F. E. Udwadia and R. E. Kalaba, "Analytical Dynamics: A New Approach," Cambridge University Press, 1996.
doi: 10.1017/CBO9780511665479. |
[21] |
F. E. Udwadia and R. E. Kalaba, Explicit equations of motion for mechanical systems with non-ideal constraints, ASME J. Appl. Mech., 68 (2001), 462-467.
doi: 10.1115/1.1364492. |
[22] |
F. E. Udwadia and R. E. Kalaba, On the foundations of analytical dynamics, Int. J. Nonlin. Mech., 37 (2002), 1079-1090.
doi: 10.1016/S0020-7462(01)00033-6. |
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