Betatron oscillations are the fast transverse oscillations of a charged particle in various focusing systems: linear accelerators, storage rings, transfer channels. Oscillations are usually considered as a small deviations from the ideal reference orbit and determined by transverse forces of focusing elements i.e. depending on transverse deviation value: quadrupole magnets, electrostatic lenses, RF-fields. This transverse motion is the subject of study of electron optics. Betatron oscillations were firstly studied by D.W. Kerst and R. Serber in 1941 while commissioning the fist betatron.[1] The fundamental study of betatron oscillations was carried out by Ernest Courant, Milton S.Livingston and Hartland Snyder that lead to the revolution in high energy accelerators design by applying strong focusing principle.[2]