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单词 Duffing differential equation
释义

Duffing differential equation

中文百科

杜芬振子 Duffing equation

(重定向自Duffing differential equation)
受驱的杜芬方程的庞加莱截面表明混沌行为。
Duffing oscillator limit cycle
Duffing oscillator limit cycle phase animation
Duffing oscillator chaos

杜芬振子 Duffing oscillator是一个描写受驱振动的振动子,由非线性微分方程表示

杜芬方程列式如下:

\frac{d^2 x(t)}{d t^2}+2\gamma\frac{d x(t)}{d t}+\alpha*x(t)+\beta*x(t)^3=\delta*cos(\omega*t)

其中

  • γ控制阻尼度
  • α控制韧度
  • β控制动力的非线性度
  • δ驱动力的振幅
  • ω驱动力的圆频率
英语百科

Duffing equation 杜芬振子

(重定向自Duffing differential equation)
A Poincaré section of the forced Duffing equation suggesting chaotic behaviour

The Duffing equation (or Duffing oscillator), named after Georg Duffing, is a non-linear second-order differential equation used to model certain damped and driven oscillators. The equation is given by

where the (unknown) function x=x(t) is the displacement at time t, \dot{x} is the first derivative of x with respect to time, i.e. velocity, and \ddot{x} is the second time-derivative of x, i.e. acceleration. The numbers \delta, \alpha, \beta, \gamma and \omega are given constants.

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更新时间:2025/6/19 22:54:50