A generalization of Szebehely’s inverse problem of dynamics in dimension three
 Author
 Willy Sarlet (UGent) , Tom Mestdag (UGent) and Geoff Prince
 Organization
 Abstract
 Extending a previous paper, we present a generalization in dimension 3 of the traditional Szebehelytype 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
Downloads

1612.04638.pdf
 full text
 
 open access
 
 
 221.69 KB
Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU8530512
 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 authordate
 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 authordate (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 Szebehelytype 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 = {00344877}, 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 = {367389}, title = {A generalization of Szebehely’s inverse problem of dynamics in dimension three}, url = {http://dx.doi.org/10.1016/S00344877(17)300496}, volume = {79}, year = {2017}, }
 Altmetric
 View in Altmetric
 Web of Science
 Times cited: