Abstract
We extend Weber's approach for mechanical systems with constraints in terms of differential-geometric structures underlying higher-order tangent bundles.
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References
Abraham, R., and Marsden, J. (1978).Foundations of Mechanics, 2nd ed., Benjamin, New York.
Ambrose, W., Palais, R., and Singer, W. (1960).Anais Academia Brasileira de Ciencas,32, 163–178.
Arnold, V. I., ed. (1988).Dynamical Systems III, Encyclopaedia of Mathematical Sciences, Springer, Berlin.
Cardin, F., and Zanzotto, G. (1989).Journal of Mathematical Physics,30, 1473–1479.
Clark, R., and Bruckheimer, M. (1960).Comptes Rendus de l'Academie des Sciences Paris,251, 627–629.
de León, M., and Rodrigues, P. R. (1985).Generalized Classical Mechanics and Field Theory, North-Holland, Amsterdam.
de León, M., and Rodrigues, P. R. (1989).Methods of Differential Geometry in Analytical Mechanics, North-Holland, Amsterdam.
Dirac, P. A. M. (1964).Lectures on Quantum Mechanics, Belfer Graduate School of Science, New York.
Duistermaat, J. (1973).Fourier Integral Operators, Courant Institute of Mathematical Sciences, New York.
Eliopoulos, H. (1962).Comptes Rendus de l'Academie des Sciences Paris,255, 1563–1565.
Godbillon, C. (1969).Géométrie Différentielle et Mécanique Analytique, Hermann, Paris.
Kármán, Th., and Biot, M. A. (1940).Mathematical Methods in Engineering, McGraw-Hill, New York.
Klein, J. (1962).Annales de l'Institut Fourier (Grenoble)12, 1–124.
Kozlov, V. V. (1983).Soviet Physics Doklady,28, 735–737.
Spivak, M. (1979).A Comprehensive Introduction to Differential Geometry, Vol. 5, Publish or Perish, Berkeley, California.
Tulczyjew, W. (1975).Comptes Rendus de l'Academie des Sciences Paris A,280, 1295–1298.
Weber, R. W. (1985).Archive for Rational Mechanics and Analysis,91, 309–335.
Whittaker, E. T. (1959).A Treatise on the Analytical Dynamics of Particle and Rigid Bodies, Cambridge University Press, Cambridge.
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de León, M., Rodrigues, P.R. Higher-order mechanical systems with constraints. Int J Theor Phys 31, 1303–1313 (1992). https://doi.org/10.1007/BF00673930
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DOI: https://doi.org/10.1007/BF00673930