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

Tom Mestdag (UGent) , Willy Sarlet (UGent) and Michael Crampin (UGent)
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Abstract
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.
Keywords
Gyroscopic forces, HELMHOLTZ CONDITIONS, Dissipative forces, Helmholtz conditions, Inverse problem, Lagrangian systems, TANGENT BUNDLE, CALCULUS, EXISTENCE, EQUATIONS, DYNAMICS, GEOMETRY, DERIVATIONS, CONNECTIONS, FORMS

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Please use this url to cite or link to this publication:

MLA
Mestdag, Tom, Willy Sarlet, and Michael Crampin. “The Inverse Problem for Lagrangian Systems with Certain Non-conservative Forces.” DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS 29.1 (2011): 55–72. Print.
APA
Mestdag, T., Sarlet, W., & Crampin, M. (2011). The inverse problem for Lagrangian systems with certain non-conservative forces. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 29(1), 55–72.
Chicago author-date
Mestdag, Tom, Willy Sarlet, and Michael Crampin. 2011. “The Inverse Problem for Lagrangian Systems with Certain Non-conservative Forces.” Differential Geometry and Its Applications 29 (1): 55–72.
Chicago author-date (all authors)
Mestdag, Tom, Willy Sarlet, and Michael Crampin. 2011. “The Inverse Problem for Lagrangian Systems with Certain Non-conservative Forces.” Differential Geometry and Its Applications 29 (1): 55–72.
Vancouver
1.
Mestdag T, Sarlet W, Crampin M. The inverse problem for Lagrangian systems with certain non-conservative forces. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS. 2011;29(1):55–72.
IEEE
[1]
T. Mestdag, W. Sarlet, and M. Crampin, “The inverse problem for Lagrangian systems with certain non-conservative forces,” DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, vol. 29, no. 1, pp. 55–72, 2011.
@article{1215598,
  abstract     = {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.},
  author       = {Mestdag, Tom and Sarlet, Willy and Crampin, Michael},
  issn         = {0926-2245},
  journal      = {DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS},
  keywords     = {Gyroscopic forces,HELMHOLTZ CONDITIONS,Dissipative forces,Helmholtz conditions,Inverse problem,Lagrangian systems,TANGENT BUNDLE,CALCULUS,EXISTENCE,EQUATIONS,DYNAMICS,GEOMETRY,DERIVATIONS,CONNECTIONS,FORMS},
  language     = {eng},
  number       = {1},
  pages        = {55--72},
  title        = {The inverse problem for Lagrangian systems with certain non-conservative forces},
  url          = {http://dx.doi.org/10.1016/j.difgeo.2010.11.002},
  volume       = {29},
  year         = {2011},
}

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