| FUNDAMENTAL AREAS OF PHENOMENOLOGY(INCLUDING APPLICATIONS) |
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Poincaré-MacMillan Equations of Motion for a Nonlinear Nonholonomic Dynamical System |
| Amjad Hussain1, Syed Tauseef Mohyud-Din2*, Ahmet Yildirim3,4 |
1Department of Mathematics, Zhejiang University, Hangzhou 310027
2Department of Mathematics, HITEC University, Taxila Cantt Pakistan
3Department of Mathematics, Ege University, 35100 Bornova Izmir, Turkey
4University of South Florida, Department of Mathematics and Statistics, Tampa, FL 33620-5700, USA
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| Cite this article: |
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Syed Tauseef Mohyud-Din, Amjad Hussain, Ahmet Yildirim 2012 Chin. Phys. Lett. 29 034502 |
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Abstract MacMillan's equations are extended to Poincaré's formalism, and MacMillan's equations for nonlinear nonholonomic systems are obtained in terms of Poincaré parameters. The equivalence of the results obtained here with other forms of equations of motion is demonstrated. An illustrative example of the theory is provided as well.
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| Keywords:
45.50.-j
45.50.Dd
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Received: 23 November 2011
Published: 11 March 2012
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| PACS: |
45.50.-j
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(Dynamics and kinematics of a particle and a system of particles)
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45.50.Dd
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(General motion)
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[1] MacMillan W D 1936 Dynamics of Rigid Bodies (New York: McGraw Hill) chap X p 332
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[4] Poincaré H 1901 Compt. Rend. Acad. Sci. 132 369 (in French)
[5] Chetaev N G 1941 Prikl. Mat. i Mekh. 5 253 (in Russian)
[6] Chetaev N G 1987 Theoretical Mechanics (Moscow: Nauka)
[7] Ghori Q K and Hussain M 1973 ZAMM J. Appl. Math. Mech. 54 311
[8] Ghori Q K and Hussain M 1973 ZAMM J. Appl. Math. Mech. 53 391
[9] Rumyantsev V V 1996 J. Appl. Math. Mech. 60 899
[10] Firdaus E U and Phohomsiri P 2007 Proc. R. Soc. A 463 1421
[11] Firdaus E U and Phohomsiri P 2007 Proc. R. Soc. A 463 1435
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