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- W2028137218 abstract "We investigate the pendulum equation θ + ⋋ 2 sin θ = 0 and two approximations for it. On the one hand, we suggest that the third and fifth-order Taylor series approximations for sin θ do not yield very good differential equations to approximate the solution of the pendulum equation unless the initial conditions are appropriately chosen very small and the time interval is short. On the other, we suggest that computationally, there is no advantage taking these approximations. We further justify this by employing an approach to deriving Fourier series approximations to the pendulum equation accurate to at least eleven decimal places. Students can generate highly accurate Fourier series solutions to nonlinear equations and thus concentrate on the qualitative aspects of the model rather than the computational difficulties." @default.
- W2028137218 created "2016-06-24" @default.
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- W2028137218 date "2002-07-01" @default.
- W2028137218 modified "2023-09-26" @default.
- W2028137218 title "The pendulum equation" @default.
- W2028137218 cites W2042254983 @default.
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- W2028137218 doi "https://doi.org/10.1080/00207390210130868" @default.
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