Author: Dmitry V. Zenkov
Publisher: Springer
ISBN: 9462391092
Category : Mathematics
Languages : en
Pages : 296
Book Description
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).
The Inverse Problem of the Calculus of Variations for Ordinary Differential Equations
Author: Ian Anderson
Publisher: American Mathematical Soc.
ISBN: 082182533X
Category : Mathematics
Languages : en
Pages : 122
Book Description
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.
Publisher: American Mathematical Soc.
ISBN: 082182533X
Category : Mathematics
Languages : en
Pages : 122
Book Description
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
Author: Dmitry V. Zenkov
Publisher: Springer
ISBN: 9462391092
Category : Mathematics
Languages : en
Pages : 296
Book Description
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).
Publisher: Springer
ISBN: 9462391092
Category : Mathematics
Languages : en
Pages : 296
Book Description
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).
Studies of the Inverse Problem of the Calculus of Variations
Author: Nathan Abraham Moscovitch
Publisher:
ISBN:
Category : Calculus of variations
Languages : en
Pages : 39
Book Description
Publisher:
ISBN:
Category : Calculus of variations
Languages : en
Pages : 39
Book Description
An Inverse Problem of the Calculus of Variations
Author: Lincoln La Paz
Publisher:
ISBN:
Category : Calculus of variations
Languages : en
Pages : 72
Book Description
Publisher:
ISBN:
Category : Calculus of variations
Languages : en
Pages : 72
Book Description
Inverse Problem of the Calculus of Variations
Certain Inverse Problems in the Calculus of Variations
Aspects of the Inverse Problem in the Calculus of Variations
Author: Jonathan E. Aldridge
Publisher:
ISBN:
Category : Calculus of variations
Languages : en
Pages : 181
Book Description
Publisher:
ISBN:
Category : Calculus of variations
Languages : en
Pages : 181
Book Description
An Approach to the Inverse Problem of the Calculus of Variation
Author: Stuart Winston Hartfield
Publisher:
ISBN:
Category : Calculus of variations
Languages : en
Pages : 54
Book Description
Publisher:
ISBN:
Category : Calculus of variations
Languages : en
Pages : 54
Book Description
The Inverse Problem of the Calculus of Variations in Higher Space
Author: David Roy Davis
Publisher:
ISBN:
Category : Calculus of variations
Languages : en
Pages : 62
Book Description
Publisher:
ISBN:
Category : Calculus of variations
Languages : en
Pages : 62
Book Description
The Calculus of Variations
Author: Bruce van Brunt
Publisher: Springer Science & Business Media
ISBN: 0387216979
Category : Mathematics
Languages : en
Pages : 295
Book Description
Suitable for advanced undergraduate and graduate students of mathematics, physics, or engineering, this introduction to the calculus of variations focuses on variational problems involving one independent variable. It also discusses more advanced topics such as the inverse problem, eigenvalue problems, and Noether’s theorem. The text includes numerous examples along with problems to help students consolidate the material.
Publisher: Springer Science & Business Media
ISBN: 0387216979
Category : Mathematics
Languages : en
Pages : 295
Book Description
Suitable for advanced undergraduate and graduate students of mathematics, physics, or engineering, this introduction to the calculus of variations focuses on variational problems involving one independent variable. It also discusses more advanced topics such as the inverse problem, eigenvalue problems, and Noether’s theorem. The text includes numerous examples along with problems to help students consolidate the material.