The Geometry of Ordinary Variational Equations

Olga Krupkova (Autor)

Buch | Softcover

CCLXIV, 254 Seiten

1997 | 1997
Springer Berlin (Verlag)
978-3-540-63832-2 (ISBN)

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The book provides a comprehensive theory of ODE which come as Euler-Lagrange equations from generally higher-order Lagrangians. Emphasis is laid on applying methods from differential geometry (fibered manifolds and their jet-prolongations) and global analysis (distributions and exterior differential systems). Lagrangian and Hamiltonian dynamics, Hamilton-Jacobi theory, etc., for any Lagrangian system of any order are presented. The key idea - to build up these theories as related with the class of equivalent Lagrangians - distinguishes this book from other texts on higher-order mechanics. The reader should be familiar with elements of differential geometry, global analysis and the calculus of variations.

Basic geometric tools.- Lagrangean dynamics on fibered manifolds.- Variational Equations.- Hamiltonian systems.- Regular Lagrangean systems.- Singular Lagrangean systems.- Symmetries of Lagrangean systems.- Geometric intergration methods.- Lagrangean systems on ?: R×M"R.

Erscheint lt. Verlag	27.11.1997
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	CCLXIV, 254 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	346 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
	Technik ► Maschinenbau
Schlagworte	Calculus • differential equation • Differential Geometry • hamiltonian mechanics • Hamilton-Jacobi theory • higher-order variational equations • Lagrangian mechanics • manifold • regularity • Variationsrechnung
ISBN-10	3-540-63832-6 / 3540638326
ISBN-13	978-3-540-63832-2 / 9783540638322
Zustand	Neuware