[1] Zhang Yi, Xue Yun,. Conserved quantities from Lie symmetriesfor nonholonomic systems [J]. Journal of Southeast University (English Edition), 2003, 19 (3): 289-292. [doi:10.3969/j.issn.1003-7985.2003.03.017]

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Conserved quantities from Lie symmetriesfor nonholonomic systems()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

19

Issue:

2003 3

Page:

289-292

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2003-09-30

Info

Title:

Conserved quantities from Lie symmetriesfor nonholonomic systems

Author(s):

Zhang Yi¹;  Xue Yun²

¹Department of Civil Engineering, University of Science and Technology of Suzhou, Suzhou 215011, China
²Department of Mechanical Engineering, Shanghai Institute of Applied Technology, Shanghai 200233, China

Keywords:

analytical mechanics;  nonholonomic system;  symmetry;  conserved quantity

PACS:

O316

DOI:

10.3969/j.issn.1003-7985.2003.03.017

Abstract:

This paper presents a new method to seek the conserved quantity from a Lie symmetry without using either Lagrangians or Hamiltonians for nonholonomic systems. The differential equations of motion of the systems are established. The definition of the Lie symmetrical transformations of the systems is given, which only depends upon the infinitesimal transformations of groups for the generalized coordinates. The conserved quantity is directly constructed in terms of the Lie symmetry of the systems. The condition under which the Lie symmetry can lead to the conserved quantity and the form of the conserved quantity are obtained. Finally, an example is given to illustrate the application of the result.

References:

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[2] Mei F X. Applications of Lie groups and Lie algebras to constrained mechanical systems [M]. Beijing: Science Press, 1999.(in Chinese)
[3] Zhao Y Y, Mei F X. Symmetries and invariants of mechanical systems[M]. Beijing: Science Press, 1999.(in Chinese)
[4] Mei F X. Lie symmetries and conserved quantities of nonholonomic systems with servoconstraints [J]. Acta Physica Sinica, 2000, 49(7): 1207-1210.(in Chinese)
[5] Zhang Y, Mei F X. Lie symmetries of mechanical systems with unilateral holonomic constraints [J]. Chinese Science Bulletin, 2000, 45(15): 1354-1358.
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[7] Zhang Y, Shang M, Mei F X. Symmetries and conserved quantities for systems of generalized classical mechanics [J]. Chinese Physics, 2000, 9(6): 401-407.
[8] Hojman S A. A new conservation law constructed without using either Lagrangians or Hamiltonians [J]. J Phys A: Math Gen, 1992, 25: L291-L295.
[9] Lutzky M. Conserved quantities from non-Noether symmetries without alternative Lagrangians [J]. International Journal of Non-Linear Mechanics, 1999, 34:387-390.
[10] Lutzky M. Conserved quantities and velocity-dependent symmetries in Lagrangian dynamics [J]. International Journal of Non-Linear Mechanics, 1998, 33(2):393-396.
[11] Zhang Y. A set of conserved quantities from Lie symmetries for Birkhoffian systems [J]. Acta Physica Sinica, 2002, 51(3): 461-464.(in Chinese)
[12] Zhang Y. A new type of conservation laws for Hamiltonian systems [J]. Chinese Quarterly of Mechanics, 2002, 23(3): 392-396.(in Chinese)

Memo

Memo:

Biography: Zhang Yi(1964—), male, doctor, professor, weidiezh@pub.sz.jsinfo.net.

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