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Symmetries and the inverse problem of Lagrangian dynamics for linear systems

Published online by Cambridge University Press:  17 February 2009

W. Sarlet
W. Sarlet
Affiliation:
Instituut voor Theoretische Mechanica. Rijksuniversiteit Gent, Krijgslaan 281 S-9, B-9000 Gent, Belgium.
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Abstract

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We discuss general, time-dependent, linear systems of second-order ordinary differential equations. A study is made of the similarities and discrepancies between the inverse problem of Lagrangian mechanics on the one hand, and the search for linear dynamical symmetries on the other hand.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 25 , Issue 2 , October 1983 , pp. 232 - 243
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Günther, N. J. and Leach, P. G. L., “Generalized invariants for the time-dependent harmonic oscillator”, J. Math. Phys. 18 (1977), 572–576.CrossRefGoogle Scholar
[2]Henneaux, M., “Equations of motion, commutation relations and ambiguities in the Lagrangian formulism”, Ann. Physics 140 (1982), 45–64.CrossRefGoogle Scholar
[3]Kwatny, H. G., Bahar, L. Y. and Massimo, F. M., “Linear non-conservative systems with asymmetric parameters derivable from a Lagrangian”, Hadronic J. 2 (1979), 1159–1177.Google Scholar
[4]Novak, L. A. and Milić, M. M., “On the existence of variational formulation for general time-varying systems”, Proc. 1980 IEEE Internar. Symp. on Circuits and Systems (Houston, Texas) (1980), 830–832.Google Scholar
[5]Sarlet, W., “Symmetries, first integrals and the inverse problem of Lagrangian mechanics”, J. Phy. A 14 (1981), 2227–2238.CrossRefGoogle Scholar
[6]Sarlet, W., “The Helmholtz conditions revisited. A new approach to the inverse problem of Lagrangian dynamics”, J. Phys. A 15 (1982), 1503–1517.CrossRefGoogle Scholar
[7]Sarlet, W.. “Note on linear systems derivable from a variational principle”, Phys. Lett., (to appear).Google Scholar
[8]Sarlet, W. and Bahar, L. Y., “Quadratic integrals for linear non-conservative systems and their connection with the inverse problem of Lagrangian dynamics”, Internat. J. Non-Linear Mech. 16 (1981), 271–281.CrossRefGoogle Scholar
[9]Sarlet, W. and Cantrijn, F., “Generalizations of Noether's theorem in classical mechanics”, SIAM Rev. 23 (1981), 467–494.CrossRefGoogle Scholar
[10]Sarlet, W., Engels, E. and Bahar, L. Y., “Time-dependent linear systems derivable from a variational principle”, Internat. J. Engrg. Sci. 20 (1982), 55–66.CrossRefGoogle Scholar