The Inverse Problem of the Calculus of Variations for Ordinary Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Inverse Problem of the Calculus of Variations for Ordinary Differential Equations write by Ian Anderson. This book was released on 1992. The Inverse Problem of the Calculus of Variations for Ordinary Differential Equations available in PDF, EPUB and Kindle. This monograph explores various aspects of the inverse problem of the calculus of variations for systems of ordinary differential equations. The main problem centres on determining the existence and degree of generality of Lagrangians whose system of Euler-Lagrange equations coicides with a given system of ordinary differential equations. The authors rederive the basic necessary and sufficient conditions of Douglas for second order equations and extend them to equations of higher order using methods of the variational bicomplex of Tulcyjew, Vinogradov, and Tsujishita. The authors present an algorithm, based upon exterior differential systems techniques, for solving the inverse problem for second order equations. a number of new examples illustrate the effectiveness of this approach.
The Inverse Problem of the Calculus of Variations
The Inverse Problem of the Calculus of Variations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Inverse Problem of the Calculus of Variations write by Dmitry V. Zenkov. This book was released on 2015-10-15. The Inverse Problem of the Calculus of Variations available in PDF, EPUB and Kindle. The aim of the present book is to give a systematic treatment of the inverse problem of the calculus of variations, i.e. how to recognize whether a system of differential equations can be treated as a system for extremals of a variational functional (the Euler-Lagrange equations), using contemporary geometric methods. Selected applications in geometry, physics, optimal control, and general relativity are also considered. The book includes the following chapters: - Helmholtz conditions and the method of controlled Lagrangians (Bloch, Krupka, Zenkov) - The Sonin-Douglas's problem (Krupka) - Inverse variational problem and symmetry in action: The Ostrogradskyj relativistic third order dynamics (Matsyuk.) - Source forms and their variational completion (Voicu) - First-order variational sequences and the inverse problem of the calculus of variations (Urban, Volna) - The inverse problem of the calculus of variations on Grassmann fibrations (Urban).
Ordinary Differential Equations and Calculus of Variations
Ordinary Differential Equations and Calculus of Variations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Ordinary Differential Equations and Calculus of Variations write by M. V. Makarets. This book was released on 1995. Ordinary Differential Equations and Calculus of Variations available in PDF, EPUB and Kindle. This problem book contains exercises for courses in differential equations and calculus of variations at universities and technical institutes. It is designed for non-mathematics students and also for scientists and practicing engineers who feel a need to refresh their knowledge. The book contains more than 260 examples and about 1400 problems to be solved by the students ? much of which have been composed by the authors themselves. Numerous references are given at the end of the book to furnish sources for detailed theoretical approaches, and expanded treatment of applications.
Inverse Problems in Ordinary Differential Equations and Applications
Inverse Problems in Ordinary Differential Equations and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Inverse Problems in Ordinary Differential Equations and Applications write by Jaume Llibre. This book was released on 2016-03-09. Inverse Problems in Ordinary Differential Equations and Applications available in PDF, EPUB and Kindle. This book is dedicated to study the inverse problem of ordinary differential equations, that is it focuses in finding all ordinary differential equations that satisfy a given set of properties. The Nambu bracket is the central tool in developing this approach. The authors start characterizing the ordinary differential equations in R^N which have a given set of partial integrals or first integrals. The results obtained are applied first to planar polynomial differential systems with a given set of such integrals, second to solve the 16th Hilbert problem restricted to generic algebraic limit cycles, third for solving the inverse problem for constrained Lagrangian and Hamiltonian mechanical systems, fourth for studying the integrability of a constrained rigid body. Finally the authors conclude with an analysis on nonholonomic mechanics, a generalization of the Hamiltonian principle, and the statement an solution of the inverse problem in vakonomic mechanics.
Numerical Treatment of Inverse Problems in Differential and Integral Equations
Numerical Treatment of Inverse Problems in Differential and Integral Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Numerical Treatment of Inverse Problems in Differential and Integral Equations write by Deuflhard. This book was released on 2012-12-06. Numerical Treatment of Inverse Problems in Differential and Integral Equations available in PDF, EPUB and Kindle. In many scientific or engineering applications, where ordinary differen tial equation (OOE),partial differential equation (POE), or integral equation (IE) models are involved, numerical simulation is in common use for prediction, monitoring, or control purposes. In many cases, however, successful simulation of a process must be preceded by the solution of the so-called inverse problem, which is usually more complex: given meas ured data and an associated theoretical model, determine unknown para meters in that model (or unknown functions to be parametrized) in such a way that some measure of the "discrepancy" between data and model is minimal. The present volume deals with the numerical treatment of such inverse probelms in fields of application like chemistry (Chap. 2,3,4, 7,9), molecular biology (Chap. 22), physics (Chap. 8,11,20), geophysics (Chap. 10,19), astronomy (Chap. 5), reservoir simulation (Chap. 15,16), elctrocardiology (Chap. 14), computer tomography (Chap. 21), and control system design (Chap. 12,13). In the actual computational solution of inverse problems in these fields, the following typical difficulties arise: (1) The evaluation of the sen sitivity coefficients for the model. may be rather time and storage con suming. Nevertheless these coefficients are needed (a) to ensure (local) uniqueness of the solution, (b) to estimate the accuracy of the obtained approximation of the solution, (c) to speed up the iterative solution of nonlinear problems. (2) Often the inverse problems are ill-posed. To cope with this fact in the presence of noisy or incomplete data or inev itable discretization errors, regularization techniques are necessary.
