TY - JOUR TI - Harmonic balancing approach to nonlinear oscillations of a punctual charge in the electric field of charged ring AU - Beléndez, Augusto AU - Fernandez-Varo, Helena AU - Rodes Roca, José Joaquín AU - Fuentes Rosillo, Rosa AU - Pascual, Inmaculada DA - 2008-12-31 UR - http://hdl.handle.net/10045/9125 AB - The harmonic balance method is used to construct approximate frequency-amplitude relations and periodic solutions to an oscillating charge in the electric field of a ring. By combining linearization of the governing equation with the harmonic balance method, we construct analytical approximations to the oscillation frequencies and periodic solutions for the oscillator. To solve the nonlinear differential equation, firstly we make a change of variable and secondly the differential equation is rewritten in a form that does not contain the square-root expression. The approximate frequencies obtained are valid for the complete range of oscillation amplitudes and excellent agreement of the approximate frequencies and periodic solutions with the exact ones are demonstrated and discussed. KW - Nonlinear oscillator KW - Harmonic balance method KW - Approximate frequency DO - 10.1016/j.physleta.2008.12.042 SN - 0375-9601 (Print) PB - Elsevier ER -