メンデレーエフの不等式
化学元素の周期表で知られるドミトリ・メンデレーエフは、補間に関する疑問から多項式とその導関数に関する定理を発見した。この数学的定理は、経験的研究に端を発し、ボアスの論文を通じて紹介されている。
関連記事
The article presents the exact closed-form solution for the nonlinear (large-angle) pendulum using Jacobi elliptic functions, contrasting it with the common small-angle approximation that uses sine functions. It explains how the exact solution involves elliptic integrals and Jacobi sn, cn, and dn functions, providing formulas for the angular displacement and period.
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The article discusses how the nonlinear behavior of a pendulum deviates from the simple harmonic oscillator approximation, particularly at large amplitudes where the period depends on the amplitude. It explains that this nonlinearity means the small-angle approximation (sinθ ≈ θ) breaks down, leading to longer periods than predicted by the linearized model.
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