caa a22 4500 467986894 CHVBK 20180323112534.0 cr unu---uuuuu 170328e19900901xx s 000 0 eng 10.1007/BF00049418 doi (NATIONALLICENCE)springer-10.1007/BF00049418 On Szebehely's problem for holonomic systems involving generalized potential functions [Elektronische Daten] [Francesco Borghero, Antonio Melis] We consider the problem of finding the generalized potential function V = U i(q 1, q 2,..., q n)q i + U(q 1, q 2,...;q n) compatible with prescribed dynamical trajectories of a holonomic system. We obtain conditions necessary for the existence of solutions to the problem: these can be cast into a system of n − 1 first order nonlinear partial differential equations in the unknown functions U 1, U 2,...;, U n, U. In particular we study dynamical systems with two degrees of freedom. Using ‘adapted' coordinates on the configuration manifold M 2 we obtain, for potential function U(q 1, q 2), a classic first kind of Abel ordinary differential equation. Moreover, we show that, in special cases of dynamical interest, such an equation can be solved by quadrature. In particular we establish, for ordinary potential functions, a classical formula obtained in different way by Joukowsky for a particle moving on a surface. Kluwer Academic Publishers, 1990 Inverse problem nationallicence generalized potential nationallicence holonomic systems nationallicence Borghero Francesco Department of Mathematics, University of Cagliari, Italy aut Melis Antonio Department of Mathematics, University of Cagliari, Italy aut Celestial Mechanics and Dynamical Astronomy Kluwer Academic Publishers 49/3(1990-09-01), 273-284 0923-2958 49:3<273 1990 49 10569 https://doi.org/10.1007/BF00049418 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00049418 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Borghero Francesco Department of Mathematics, University of Cagliari, Italy aut NATIONALLICENCE 700 1- Melis Antonio Department of Mathematics, University of Cagliari, Italy aut NATIONALLICENCE 773 0- Celestial Mechanics and Dynamical Astronomy Kluwer Academic Publishers 49/3(1990-09-01), 273-284 0923-2958 49:3<273 1990 49 10569 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer