Geodesic
Averaging equations of betatron oscillations in the vicinity of resonances in cyclic accelerators
Matematičeskoe modelirovanie, Tome 2 (1990) no. 3, pp. 43-54.

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The algorithm for computer generation of equations of motion for charge particle small deviations from the closed orbit in cyclic accelerator is presented. The realized with the help of REDUCE-3.2 method of averaging in high approximations which it applied to the generated equations of motion is described. The averaging equations in the vicinity of 19 resonances for JINR synchrophasotron and the averging equations in the vicinity of 24 resonances for JINR nuclotron, generated by the programs based on the described algorithms are represented. Some investigation methods for these averaging equations are proposed. 
@article{MM_1990_2_3_a4,
     author = {I. V. Amirkhanov and E. P. Zhidkov and I. E. Zhidkova},
     title = {Averaging equations of betatron oscillations in the vicinity of resonances in cyclic accelerators},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {43--54},
     publisher = {mathdoc},
     volume = {2},
     number = {3},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1990_2_3_a4/}
}
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I. V. Amirkhanov; E. P. Zhidkov; I. E. Zhidkova. Averaging equations of betatron oscillations in the vicinity of resonances in cyclic accelerators. Matematičeskoe modelirovanie, Tome 2 (1990) no. 3, pp. 43-54. http://geodesic.mathdoc.fr/item/MM_1990_2_3_a4/