Geodesic
First Integrals of Lorentz Equations for Certain Classes of Electromagnetic Fields
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 236 (2002), pp. 197-203

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By the method developed by one of the authors, sets of first integrals of equations of motion are obtained for a charged test particle in electromagnetic fields of certain classes. 
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     author = {A. S. Ivanova and M. A. Parinov},
     title = {First {Integrals} of {Lorentz} {Equations} for {Certain} {Classes} of {Electromagnetic} {Fields}},
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A. S. Ivanova; M. A. Parinov. First Integrals of Lorentz Equations for Certain Classes of Electromagnetic Fields. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 236 (2002), pp. 197-203. http://geodesic.mathdoc.fr/item/TM_2002_236_a19/