| 从立方抛物线谈起(1)--余弦型振动,椭圆余弦型振动与双曲线型非周期运动 |
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| 引用本文： | 佘守宪.从立方抛物线谈起(1)--余弦型振动,椭圆余弦型振动与双曲线型非周期运动[J].物理与工程,2003,13(2). |
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| 作者姓名： | 佘守宪 |
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| 作者单位： | 北方交通大学物理系,北京,100044 |
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| 摘 要： | 从立方抛物线的特性谈起 ,用较初浅的方法 ,借助于雅可比椭圆函数求椭圆方程的解来说明一大类一维保守系统的余弦振动、椭圆余弦型振动与双曲线型非周期运动 .并以杜芬振子、单摆、倒摆、转动圆环上的小环运动为典型实例作了详细讨论
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| 关 键 词： | 非线性振动 立方抛物线 雅可比椭圆函数 椭圆方程 |
STARTING FROM CUBIC PARABOLA (1) |
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| She Shouxian.STARTING FROM CUBIC PARABOLA (1)[J].Physics and Engineering,2003,13(2). |
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| Authors: | She Shouxian |
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| Abstract: | Starting with properties of cubic parabola, we solved elementarily the elliptic equations using Jacobian function for one\|dimensional conservative system. we obtained the analytic solutions for sinusoidal vibrations, cnoidal vibrations and hyperbolic motion. We discussed some typical examples such as Duffing oscillator, simple pendulum, inverted pendulum, and particle on a rotating circle. |
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| Keywords: | nonlinear vibrations cubic parabola Jacobian elliptic function elliptic equations |
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