초기 각변위 및 각속도 조건에 대한 비선형 단진자의 일반 엄밀해
General Exact Solution of the Nonlinear Simple Pendulum for Initial Angular Position and Velocity Conditions
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The nonlinear simple pendulum is investigated to find the exact closed-form analytical solution, satisfying initial conditions of angular position and angular velocity. While previous numerous studies have been conducted on the nonlinear simple pendulum, the exact closed-form analytical solution still remains not available in public domain for the most general initial condition including initial angular velocity as well as initial angular displacement. In this paper, the exact closed-form analytical solution for the general initial conditions is derived using Jacobi’s elliptic function and elliptic integral. The result was verified by comparing it with previous studies and the numerical solution of the equation of motion through the Runge-Kutta integration method.
Abstract
The nonlinear simple pendulum is investigated to find the exact closed-form analytical solution, satisfying initial conditions of angular position and angular velocity. While previous numerous studies have been conducted on the nonlinear simple pendulum, the exact closed-form analytical solution still remains not available in public domain for the most general initial condition including initial angular velocity as well as initial angular displacement. In this paper, the exact closed-form analytical solution for the general initial conditions is derived using Jacobi’s elliptic function and elliptic integral. The result was verified by comparing it with previous studies and the numerical solution of the equation of motion through the Runge-Kutta integration method.
참고문헌 (4)
- A. Beléndez, "Analytical approximations for the period of a nonlinear pendulum", European of Journal of Physics, 27(3), pp.539~ (2006)
- A. Beléndez, "Exact solution for the nonlinear pendulum", Revista Brasileira de Ensino de Fisica, 29(4), pp.645~648 (2007)
- Karlheinz Ochs, "A comprehensive analytical solution of the nonlinear pendulum", Eur. J. Phys, 32, pp.479~490 (2011)
- Mohammad Asadi Dalir, "General Exact Closed-Form Solution for Nonlinear Differential Equation of Pendulum", Natl. Acad. Sci. Lett (2020)