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Study of Theory about Large Unified Symmetries for Hamilton Systems

Published online by Cambridge University Press:  16 June 2011

Y.-P. Luo
Y.-P. Luo*
Affiliation:
Department of Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China
*
*Associate Professor, corresponding author
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Abstract

In this paper, the new concept of theory about Large Unified Symmetries for Hamilton systems are presented. The Large Unified Symmetries and conserved quantities for Hamilton systems are studied by the relation between the three kinds of symmetries and the three kinds of conserved quantities. We worked on the Large Unified Symmetries and conserved quantities by Noether symmetry, Lie symmetry and Mei symmetry, including the definition and criterion of the Large Unified Symmetries and the conserved quantities deduced from them. The Large Unified Symmetries are a intersection set among the Noether symmetries, the Lie symmetries and the Mei symmetries. The theory about Large Unified Symmetries will play an important role in the fields of modern theoretical physics.

Keywords

Large Unified SymmetryInvarianceConserved quantityHamilton system
Type
Articles
Information
Journal of Mechanics , Volume 27 , Issue 2 , June 2011 , pp. 245 - 252
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2011

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References

1. Galiullin, A. S., Gafarov, G. G., Malaishka, R. P. and Khwan, A. M., Analytical Dynamics of Helm-holtz, Birkhoff and Nambu Systems, Moscow, UFN (1997).Google Scholar
2. Zhang, Y., Shang, M. and Mei, F. X., “Symmetries and Conserved Quantities for Systems of Generalized Classical Mechanics,” Chinese Physics B, 9, pp. 401–407 (2000).Google Scholar
3. Lou, Z. M., “The Study of Symmetries and Conserved Quantities for One-Dimensional Damped-Amplified Harmonic Oscillators,” Acta Physica Sinica, 57, pp. 1307–1310 (2008).Google Scholar
4. Cai, J. L., “Conformal Invariance and Conserved Quantities of Mei Symmetry for Lagrange Systems,” Acta Physica Polonica A, 115, pp. 854–856 (2009).CrossRefGoogle Scholar
5. Pang, T., Fang, J. H., Zhang, M. J., Lin, P. and Lu, K., “A New Type of Conserved Quantity Deduced from Mei Symmetry of Nonholonomic Systems in Terms of Quasi-Coordinates,” Chinese Physics B, 18, pp. 3150–3154 (2009).Google Scholar
6. Zhang, Y., “Conformal Invariance and Noether Symmetry, Lie Symmetry of Holonomic Mechanical Systems in Event Space,” Chinese Physics B, 18, pp. 4636–4642 (2009).Google Scholar
7. Hou, Q. B., Li, Y. C., Wang, J. and Xia, L. L., “Unified Symmetry of the Nonholonomic System of Non-Chetaev Type with Unilateral Constraints in Event Space,” Chinese Physics B, 16, pp. 1521–1525 (2007).Google Scholar
8. Fu, J. Li., Zhao, W. J. and Weng, Y. Q., “Structure Properties and Noether Symmetries for Super-Long Elastic Slender Rod,” Chinese Physics B, 17, pp. 2361–2365 (2008).Google Scholar
9. Chen, X. W., Liu, C. and Mei, F. X., “Conformal Invariance and Hojman Conserved Quantities of First Order Lagrange Systems,” Chinese Physics B, 17, pp. 3180–3184 (2008).Google Scholar
10. Luo, S. K., Cai, J. L. and Jia, L. Q., “Adiabatic In-variants of Generalized Lutzky Type for Disturbed Holonomic Nonconservative Systems,” Chinese Physics B, 17, pp. 3542–3548 (2008).Google Scholar
11. Shi, S. Y., Fu, J. L. and Chen, Q., “The Lie Symmetries and Noether Conserved Quantities of Discrete Non-Conservative Mechanical Systems,” Chinese Physics B, 17, pp. 385–389 (2008).Google Scholar
12. Chen, X. W., Zhao, Y. H. and Liu, C., “Conformal Invariance and Conserved Quantity for Holonomic Mechanical Systems with Variable Mass,” Acta Physica Sinica, 58, pp. 5150–5154 (2009).CrossRefGoogle Scholar
13. Ge, W. K., “Mei Symmetry and Conserved Quantity of a Holonomic System,” Acta Physica Sinica, 57, pp. 6714–6717 (2008).Google Scholar
14. Liu, Y. C., Xia, L. and Wang, X. M., “Unified Symmetry of Mechanico-Electrical Systems with Nonholonomic Constraints of Non-Chetaev's Type,” Acta Physica Sinica, 58, pp. 6732–6736 (2009).Google Scholar
15. Luo, Y. P., “Generalized Conformal Symmetries and its Application of Hamilton Systems,” International Journal of Theoretical Physics, 48, pp. 2665–2671 (2009).CrossRefGoogle Scholar
16. Jia, L. Q., Zhang, Y. Y., Cui, J. C. and Luo, S.K., “Structural Equation and Mei Conserved Quantity of Mei Symmetry for Appell Equations in Holonomic Systems with Unilateral Constraints,” Communications in Theoretical Physics, 55, pp. 572–576 (2009).Google Scholar
17. Ding, N. and Fang, J. H., “A New Type of Mei Adiabatic Invariant Induced by Perturbation to Mei Symmetry of Hamiltonian Systems,” Communications in Theoretical Physics, 52, pp. 12–16 (2009).Google Scholar
18. Wan, W. T. and Chen, Y., “A Note on Nonclassical Symmetries of a Class of Nonlinear Partial Differential Equations and Compatibility,” Communications in Theoretical Physics, 52, pp. 398–402 (2009).Google Scholar
19. Mei, J. Q., “Noether-Type Symmetries and Associated Conservation Laws of Some Systems of Nonlinear PDEs,” Communications in Theoretical Physics, 51, pp. 495–498 (2009).Google Scholar
20. Liu, P., “Symmetries and Similarity Reductions of aNew (2 + 1)-Dimensional Shallow Water Wave System,” Communications in Theoretical Physics, 49, pp. 555–558 (2008).Google Scholar