Geodesic
Integrable newtonian systems with nonpotential force fields
Matematičeskoe modelirovanie, Tome 18 (2006) no. 5, pp. 126-128.

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Integrable Newtonian systems with nonpotential force fields, which have two first integrals quadratic by momenta, are studied. The explicit expressions for force fields are received. Dynamic equations are integrated in quadratures. 
@article{MM_2006_18_5_a10,
     author = {A. A. Zaitsev and E. V. Zaitseva},
     title = {Integrable newtonian systems with nonpotential force fields},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {126--128},
     publisher = {mathdoc},
     volume = {18},
     number = {5},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2006_18_5_a10/}
}
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A. A. Zaitsev; E. V. Zaitseva. Integrable newtonian systems with nonpotential force fields. Matematičeskoe modelirovanie, Tome 18 (2006) no. 5, pp. 126-128. http://geodesic.mathdoc.fr/item/MM_2006_18_5_a10/