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A generalization of Szebehely’s inverse problem of dynamics in dimension three

Willy Sarlet (UGent) , Tom Mestdag (UGent) and Geoff Prince
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Abstract
Extending a previous paper, we present a generalization in dimension 3 of the traditional Szebehely-type inverse problem. In that traditional setting, the data are curves determined as the intersection of two families of surfaces, and the problem is to find a potential V such that the Lagrangian L = T - V, where T is the standard Euclidean kinetic energy function, generates integral curves which include the given family of curves. Our more general way of posing the problem makes use of ideas of the inverse problem of the calculus of variations and essentially consists of allowing more general kinetic energy functions, with a metric which is still constant, but need not be the standard Euclidean one. In developing our generalization, we review and clarify different aspects of the existing literature on the problem and illustrate the relevance of the newly introduced additional freedom with many examples.
Keywords
Szebehely's equation, inverse problem of dynamics, inverse problem of the calculus of variations

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MLA
Sarlet, Willy, Tom Mestdag, and Geoff Prince. “A Generalization of Szebehely’s Inverse Problem of Dynamics in Dimension Three.” REPORTS ON MATHEMATICAL PHYSICS 79.3 (2017): 367–389. Print.
APA
Sarlet, Willy, Mestdag, T., & Prince, G. (2017). A generalization of Szebehely’s inverse problem of dynamics in dimension three. REPORTS ON MATHEMATICAL PHYSICS, 79(3), 367–389.
Chicago author-date
Sarlet, Willy, Tom Mestdag, and Geoff Prince. 2017. “A Generalization of Szebehely’s Inverse Problem of Dynamics in Dimension Three.” Reports on Mathematical Physics 79 (3): 367–389.
Chicago author-date (all authors)
Sarlet, Willy, Tom Mestdag, and Geoff Prince. 2017. “A Generalization of Szebehely’s Inverse Problem of Dynamics in Dimension Three.” Reports on Mathematical Physics 79 (3): 367–389.
Vancouver
1.
Sarlet W, Mestdag T, Prince G. A generalization of Szebehely’s inverse problem of dynamics in dimension three. REPORTS ON MATHEMATICAL PHYSICS. 2017;79(3):367–89.
IEEE
[1]
W. Sarlet, T. Mestdag, and G. Prince, “A generalization of Szebehely’s inverse problem of dynamics in dimension three,” REPORTS ON MATHEMATICAL PHYSICS, vol. 79, no. 3, pp. 367–389, 2017.
@article{8530512,
  abstract     = {Extending a previous paper, we present a generalization in dimension 3 of the traditional Szebehely-type inverse problem. In that traditional setting, the data are curves determined as the intersection of two families of surfaces, and the problem is to find a potential V such that the Lagrangian L = T - V, where T is the standard Euclidean kinetic energy function, generates integral curves which include the given family of curves. Our more general way of posing the problem makes use of ideas of the inverse problem of the calculus of variations and essentially consists of allowing more general kinetic energy functions, with a metric which is still constant, but need not be the standard Euclidean one. In developing our generalization, we review and clarify different aspects of the existing literature on the problem and illustrate the relevance of the newly introduced additional freedom with many examples.},
  author       = {Sarlet, Willy and Mestdag, Tom and Prince, Geoff},
  issn         = {0034-4877},
  journal      = {REPORTS ON MATHEMATICAL PHYSICS},
  keywords     = {Szebehely's equation,inverse problem of dynamics,inverse problem of the calculus of variations},
  language     = {eng},
  number       = {3},
  pages        = {367--389},
  title        = {A generalization of Szebehely’s inverse problem of dynamics in dimension three},
  url          = {http://dx.doi.org/10.1016/S0034-4877(17)30049-6},
  volume       = {79},
  year         = {2017},
}

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