Harmonic-energy balance method for solving pendulum equation

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    A harmonic-energy balance method is put forward to solve the strong nonlinear pendulum equation. The difference from the classical perturbation method is that the harmonic balance method does not account the differential equation and initial conditions separately, but it considers both simultaneously. Through the harmonic-balance method, two-order ordinary differential equations describing dynamic systems become a set of nonlinear algebraic equations with the variables of angular frequency and amplitude. Considering the balance of energy, the close equations with angular frequency and amplitude as the variables can be solved. The harmonic-energy balance method is a combination of harmonic-balance and energy balance. It overcomes the shortcomings of both methods and takes their advantages. A case study also shows that the harmonicenergy balance method is simpler with higher precision although it takes less harmonics.

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  • Received:May 01,2015
  • Revised:June 08,2015
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  • Online: May 26,2016
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