VARIATIONAL PRINCIPLES FOR SECOND-ORDE.. (eBook)

Application of the Spencer Theory to Characterize Variational Sprays

Joseph Grifone, Zoltan Muzsnay (Autoren)

eBook Download: PDF

2000
228 Seiten
World Scientific Publishing Company (Verlag)
978-981-281-359-6 (ISBN)

Infos

The inverse problem of the calculus of variations was first studied by Helmholtz in 1887 and it is entirely solved for the differential operators, but only a few results are known in the more general case of differential equations. This book looks at second-order differential equations and asks if they can be written as Euler-Lagrangian equations. If the equations are quadratic, the problem reduces to the characterization of the connections which are Levi-Civita for some Riemann metric.To solve the inverse problem, the authors use the formal integrability theory of overdetermined partial differential systems in the Spencer-Quillen-Goldschmidt version. The main theorems of the book furnish a complete illustration of these techniques because all possible situations appear: involutivity, 2-acyclicity, prolongation, computation of Spencer cohomology, computation of the torsion, etc.

Produkt-Details

• Erscheint lt. Verlag: 25.5.2000
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
• ISBN-10: 981-281-359-4 / 9812813594
• ISBN-13: 978-981-281-359-6 / 9789812813596