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Books > Science & Mathematics > Mathematics > Geometry > Differential & Riemannian geometry
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The Geometry of Higher-Order Lagrange Spaces - Applications to Mechanics and Physics (Hardcover, 1997 ed.)
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The Geometry of Higher-Order Lagrange Spaces - Applications to Mechanics and Physics (Hardcover, 1997 ed.)
Series: Fundamental Theories of Physics, 82
Expected to ship within 10 - 15 working days
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Total price: R4,452
Discovery Miles: 44 520
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This monograph is mostly devoted to the problem of the geome-
trizing of Lagrangians which depend on higher order accelerations.
It naturally prolongs the theme of the monograph "The Geometry of
La- grange spaces: Theory and Applications", written together with
M. Anastasiei and published by Kluwer Academic Publishers in 1994.
The existence of Lagrangians of order k > 1 has been
contemplated by mechanicists and physicists for a long time.
Einstein had grasped their presence in connection with the Brownian
motion. They are also present in relativistic theories based on
metrics which depend on speeds and accelerations of particles or in
the Hamiltonian formulation of non- linear systems given by
Korteweg-de Vries equations. There resulted from here the methods
to be adopted in their theoretical treatment. One is based on the
variational problem involving the integral action of the
Lagrangian. A second one is derived from the axioms of Analytical
Mechanics involving the Poincare-Cartan forms. The geometrical
methods based on the study of the geometries of higher order could
invigorate the whole theory. This is the way adopted by us in
defining and studying the Lagrange spaces of higher order. The
problems raised by the geometrization of Lagrangians of order k
> 1 investigated by many scholars: Ch. Ehresmann, P. Libermann,
J. Pommaret; J.T. Synge, M. Crampin, P. Saunders; G.S. Asanov,
P.Aringazin; I. Kolar, D. Krupka; M. de Leon, W. Sarlet, P.
Cantrjin, H. Rund, W.M. Tulczyjew, A. Kawaguchi, K. Yano, K. Kondo,
D.
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