The inverse problem for Lagrangian systems with certain non-conservative forces

We discuss two generalizations of the inverse problem of the calculus of variations, one in which a given mechanical system can be brought into the form of Lagrangian equations with non-conservative forces of a generalized Rayleigh dissipation type, the other leading to Lagrangian equations with so-...

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Bibliographic Details
Published inDifferential geometry and its applications Vol. 29; no. 1; pp. 55 - 72
Main Authors Mestdag, T., Sarlet, W., Crampin, M.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.02.2011
Subjects
Calculus of variations
Dissipation
Dissipative forces
Equivalence
Gyroscopic forces
Helmholtz conditions
Inverse problem
Inverse problems
Lagrangian equations
Lagrangian systems
Mathematical analysis
Mechanical systems
Multipliers
Representations
Lagrangian systems
Dissipative forces
Gyroscopic forces
49N45
70F17
70H03
Inverse problem
Helmholtz conditions
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Summary:We discuss two generalizations of the inverse problem of the calculus of variations, one in which a given mechanical system can be brought into the form of Lagrangian equations with non-conservative forces of a generalized Rayleigh dissipation type, the other leading to Lagrangian equations with so-called gyroscopic forces. Our approach focusses primarily on obtaining coordinate-free conditions for the existence of a suitable non-singular multiplier matrix, which will lead to an equivalent representation of a given system of second-order equations as one of these Lagrangian systems with non-conservative forces.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0926-2245
1872-6984
DOI:10.1016/j.difgeo.2010.11.002