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A generalization of Szebehely’s inverse problem of dynamics

Willy Sarlet (UGent) , Tom Mestdag (UGent) and Geoff Prince
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Abstract
The so-called inverse problem of dynamics is about constructing a potential for a given family of curves. We observe that there is a more general way of posing the problem by making use of ideas of another inverse problem, namely the inverse problem of the calculus of variations. We critically review and clarify different aspects of the current state of the art of the problem (mainly restricted to the case of planar curves), and then develop our more general approach.
Keywords
HELMHOLTZ CONDITIONS, HAMILTON-JACOBI THEORY, CALCULUS, EQUATION, TRAJECTORIES, SYSTEMS, FAMILIES, ORBITS, inverse problem of the calculus of variations, inverse problem of dynamics, Szebehely's equation

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Citation

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

MLA
Sarlet, Willy, Tom Mestdag, and Geoff Prince. “A Generalization of Szebehely’s Inverse Problem of Dynamics.” REPORTS ON MATHEMATICAL PHYSICS 72.1 (2013): 65–84. Print.
APA
Sarlet, Willy, Mestdag, T., & Prince, G. (2013). A generalization of Szebehely’s inverse problem of dynamics. REPORTS ON MATHEMATICAL PHYSICS, 72(1), 65–84.
Chicago author-date
Sarlet, Willy, Tom Mestdag, and Geoff Prince. 2013. “A Generalization of Szebehely’s Inverse Problem of Dynamics.” Reports on Mathematical Physics 72 (1): 65–84.
Chicago author-date (all authors)
Sarlet, Willy, Tom Mestdag, and Geoff Prince. 2013. “A Generalization of Szebehely’s Inverse Problem of Dynamics.” Reports on Mathematical Physics 72 (1): 65–84.
Vancouver
1.
Sarlet W, Mestdag T, Prince G. A generalization of Szebehely’s inverse problem of dynamics. REPORTS ON MATHEMATICAL PHYSICS. 2013;72(1):65–84.
IEEE
[1]
W. Sarlet, T. Mestdag, and G. Prince, “A generalization of Szebehely’s inverse problem of dynamics,” REPORTS ON MATHEMATICAL PHYSICS, vol. 72, no. 1, pp. 65–84, 2013.
@article{4177964,
  abstract     = {The so-called inverse problem of dynamics is about constructing a potential for a given family of curves. We observe that there is a more general way of posing the problem by making use of ideas of another inverse problem, namely the inverse problem of the calculus of variations. We critically review and clarify different aspects of the current state of the art of the problem (mainly restricted to the case of planar curves), and then develop our more general approach.},
  author       = {Sarlet, Willy and Mestdag, Tom and Prince, Geoff},
  issn         = {0034-4877},
  journal      = {REPORTS ON MATHEMATICAL PHYSICS},
  keywords     = {HELMHOLTZ CONDITIONS,HAMILTON-JACOBI THEORY,CALCULUS,EQUATION,TRAJECTORIES,SYSTEMS,FAMILIES,ORBITS,inverse problem of the calculus of variations,inverse problem of dynamics,Szebehely's equation},
  language     = {eng},
  number       = {1},
  pages        = {65--84},
  title        = {A generalization of Szebehely’s inverse problem of dynamics},
  volume       = {72},
  year         = {2013},
}

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