Item description for Variational Principles for Second Order Differential Equations: Application of the Spencer Theory to Characterize Variational Sprays by Joseph Grifone & Zoltan Muzsnay...
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 work 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, and more.
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Studio: World Scientific Publishing Company
Est. Packaging Dimensions: Length: 0.5" Width: 6" Height: 8.5" Weight: 1 lbs.
Publisher World Scientific Publishing Company
ISBN 9810237340 ISBN13 9789810237349