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Inverse Problems in Ordinary Differential Equations and Applications

Part of the Progress in Mathematics Book Series (volume 313)

DOI: 10.1007/978-3-319-26339-7

ISBN: 978-3-319-26337-3

Publisher: Springer International Publishing - Springer Journals

Mar 10, 2016

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Chapter 1Differential Equations with Given Partial and First Integrals

Llibre, Jaume; Ramírez, Rafael

Pages: 1 –40

[In this chapter we present two different kind of results. First, under very general assumptions we characterize the ordinary differential equations in\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}...
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Chapter 2Polynomial Vector Fields with Given Partial and First Integrals

Llibre, Jaume; Ramírez, Rafael

Pages: 41 –85

[The solutions of the inverse problem in ordinary differential equations have a very high degree of arbitrariness because of the unknown functions involved. To reduce this arbitrariness we need additional conditions. In this chapter we are mainly interested in the planar polynomial differential...
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Chapter 3Hilbert’s 16th Problem for Algebraic Limit Cycles

Llibre, Jaume; Ramírez, Rafael

Pages: 87 –116

[In this chapter we state Hilbert’s 16th problem restricted to algebraic limit cycles. Namely, consider the set Σ’n of all real polynomial vector fields \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}...
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Chapter 4Inverse Problem for Constrained Lagrangian Systems

Llibre, Jaume; Ramírez, Rafael

Pages: 117 –152

[The aim of this chapter is to provide a solution of the inverse problem of the constrained Lagrangian mechanics which can be stated as follows: Determine for a given natural mechanical system with N degrees of freedom the most general field of forces depending only on the positions and...
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Chapter 5Inverse Problem for Constrained Hamiltonian Systems

Llibre, Jaume; Ramírez, Rafael

Pages: 153 –163

[Constrained Hamiltonian systems arise in many fields, for instance in multi-body dynamics or in molecular dynamics. The theory of such systems goes back to by P.A.M. Dirac (see for instance [44]).]
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Chapter 6Integrability of the Constrained Rigid Body

Llibre, Jaume; Ramírez, Rafael

Pages: 165 –199

[The integration theory of the differential equations which describe the motion of a mechanical system with constraints (constrained mechanical system) is not so complete as for mechanical systems without constraints (unconstrained mechanical systems). This can be due to several reasons. One of...
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Chapter 7Inverse Problem in Vakonomic Mechanics

Llibre, Jaume; Ramírez, Rafael

Pages: 201 –251

[The mechanical systems free of constraints are called Lagrangian systems or holonomic systems. The mechanical systems with integrable constraints are called holonomic constrained mechanical systems. Finally, the mechanical systems with non-integrable constraints are usually called nonholonomic...

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