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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. Google Scholar |
[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.
doi: 10.1007/BF03014784. |
[3] |
N. G. Chataev, "Theoretical Mechanics,", Mir Publications, (1989). Google Scholar |
[4] |
C. T. Chen, "Linear System Theory and Design,", Oxford University Press, (1999). Google Scholar |
[5] |
P. A. M. Dirac, "Lectures in Quantum Mechanics,", New York, (1964). Google Scholar |
[6] |
C. Gauss, Uber ein neues allgemeines grundgesetz der mechanik,, J. Reine Angew. Math., 4 (1829), 232.
doi: 10.1515/crll.1829.4.232. |
[7] |
W. Gibbs, On the fundamental formulae of dynamics,, Am. J. Math., 2 (1879), 49.
doi: 10.2307/2369196. |
[8] |
H. Goldstein, "Classical Mechanics,", Addison-Wesley, (1981). Google Scholar |
[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, (1949). Google Scholar |
[11] |
J. L. Lagrange, "Mechanique Analytique,", Paris: Mme Ve Courcier, (1787). Google Scholar |
[12] |
L. A. Pars, "A Treatise on Analytical Dynamics,", Woodridge, (1979). Google Scholar |
[13] |
R. Penrose, A generalized inverse of a matrices,, Proc. Cambridge Philos. Soc., 51 (1955), 406.
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).
doi: 10.1115/1.4002329. |
[15] |
E. C. G. Sudarshan and N. Mukunda, "Classical Dynamics: A Modern Perspective,", Wiley, (1974).
|
[16] |
F. E. Udwadia and A. D. Schutte, Equations of motion for general constrained systems in Lagrangian mechanics,, Acta Mechanica., 213 (2010), 111.
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.
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.
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.
|
[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.
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.
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. Google Scholar |
[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.
doi: 10.1007/BF03014784. |
[3] |
N. G. Chataev, "Theoretical Mechanics,", Mir Publications, (1989). Google Scholar |
[4] |
C. T. Chen, "Linear System Theory and Design,", Oxford University Press, (1999). Google Scholar |
[5] |
P. A. M. Dirac, "Lectures in Quantum Mechanics,", New York, (1964). Google Scholar |
[6] |
C. Gauss, Uber ein neues allgemeines grundgesetz der mechanik,, J. Reine Angew. Math., 4 (1829), 232.
doi: 10.1515/crll.1829.4.232. |
[7] |
W. Gibbs, On the fundamental formulae of dynamics,, Am. J. Math., 2 (1879), 49.
doi: 10.2307/2369196. |
[8] |
H. Goldstein, "Classical Mechanics,", Addison-Wesley, (1981). Google Scholar |
[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, (1949). Google Scholar |
[11] |
J. L. Lagrange, "Mechanique Analytique,", Paris: Mme Ve Courcier, (1787). Google Scholar |
[12] |
L. A. Pars, "A Treatise on Analytical Dynamics,", Woodridge, (1979). Google Scholar |
[13] |
R. Penrose, A generalized inverse of a matrices,, Proc. Cambridge Philos. Soc., 51 (1955), 406.
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).
doi: 10.1115/1.4002329. |
[15] |
E. C. G. Sudarshan and N. Mukunda, "Classical Dynamics: A Modern Perspective,", Wiley, (1974).
|
[16] |
F. E. Udwadia and A. D. Schutte, Equations of motion for general constrained systems in Lagrangian mechanics,, Acta Mechanica., 213 (2010), 111.
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.
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.
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.
|
[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.
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.
doi: 10.1016/S0020-7462(01)00033-6. |
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