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Opris, D.; Albu, I. D.

Geometrical aspects of the covariant dynamics of higher order. (English) Zbl 0955.53013

Czech. Math. J. 48, No. 3, 395-412 (1998).
Summary: We present some geometrical aspects of a higher-order jet bundle which is considered a suitable framework for the study of higher-order dynamics in continuous media. We generalize some results obtained by A. Vondra [Czech. Math. J. 41, 724-730 (1991; Zbl 0764.53019)]. These results lead to a description of the geometrical dynamics of higher order generated by regular equations.

MSC:

53C05 Connections (general theory)
58A20 Jets in global analysis
70H03 Lagrange’s equations

Keywords:

jet bundle; fibered manifold; field theory; geometrical dynamics

Citations:

Zbl 0764.53019
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Full Text: DOI EuDML

References:

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[2] M. Ferraris, M. Francaviglia: On the Global Structure of Lagrangian and Hamiltonian Formalisms in Higher Order Calculus of Variations, Proceedings of the Meeting “Geometry and Physics”. Florence, October 12-15 (1982), 43-70.
[3] H. Goldschmidt, S. Stemberg: The Hamilton-Cartan Formalism in the Calculus of Variations. Ann. Inst. Fourier, Grenoble 23 (1973), 203-267. · Zbl 0243.49011 · doi:10.5802/aif.451
[4] M. J. Gotay: A multisymplectic Framework for Classical Field Theory aud the Calculus of Variations. I. Covariant Hamiltonian Formalism, Mechanics, Analysis and Geometry 200 Years after Lagrange, Amsterdam, 1990.
[5] A. Vondra: Semisprays, connections and regular equations in higher order mechanics. Proc. Conf. Diff. Geom. and Its. Appl., World Scientific, Singapore (1990), 276-287. · Zbl 0809.58015
[6] A. Vondra: Some connections related to the geometry of regular higher-order dynamics. Sbornik VA Brno, Řada “B” 2 (1992), 7-18.
[7] A. Vondra: Natural Dynamical Connections. Czechoslovak Math. J., Praha 41(116) (1991), 724-730. · Zbl 0764.53019
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