ForcedPendulum
This simulink model simulates the damped driven pendulum, showing it s chaotic motion.
theta = angle of pendulum
omega = (d/dt)theta = angular velocity
Gamma(t) = gcos(phi) = Force
omega_d = (d/dt) phi
Gamma(t) = (d/dt)omega + omega/Q + sin(theta)
Play with the initial conditions (omega_0, theta_0, phi_0 = omega(t=0), theta(t=0), phi(t=0)) and the system parameters (g, Q, omega_d) and the solver parameters/method.
Chaos can be seen for Q=2, omega_d=w/3.
The program outputs to Matlab time, theta(time) & omega(time).
Plot the phase space via:
plot(mod(theta+pi, 2*pi)-pi, omega, . )
Plot the Poincare sections using:
t_P = (0:2*pi/omega_d:max(time))
plot(mod(spline(time, theta+pi, t_P), 2*pi)-pi, spline(time, omega, t_P), . )
System is described in:
"Fractal basin boundaries and intermittency in the driven damped pendulum"
E. G. Gwinn and R. M. Westervelt
PRA 33(6):4143 (1986)
(This simulink model simulates the damped driven pendulum, showing it s chaotic motion.
theta = angle of pendulum
omega = (d/dt)theta = angular velocity
Gamma(t) = gcos(phi) = Force
omega_d = (d/dt) phi
Gamma(t) = (d/dt)omega+ omega/Q+ sin(theta)
Play with the initial conditions (omega_0, theta_0, phi_0 = omega(t=0), theta(t=0), phi(t=0)) and the system parameters (g, Q, omega_d) and the solver parameters/method.
Chaos can be seen for Q=2, omega_d=w/3.
The program outputs to Matlab time, theta(time) & omega(time).
Plot the phase space via:
plot(mod(theta+pi, 2*pi)-pi, omega, . )
Plot the Poincare sections using:
t_P = (0:2*pi/omega_d:max(time))
plot(mod(spline(time, theta+pi, t_P), 2*pi)-pi, spline(time, omega, t_P), . )
System is described in:
"Fractal basin boundaries and intermittency in the driven damped pendulum"
E. G. Gwinn and R. M. Westervelt
PRA 33(6):4143 (1986)
)
- 2010-02-17 07:28:51下载
- 积分：1
GM1_1
灰色理论认为系统的行为现象尽管是朦胧的，数据是复杂的，但它毕竟是有序的，是有整体功能的。灰数的生成，就是从杂乱中寻找出规律。同时，灰色理论建立的是生成数据模型，不是原始数据模型，因此，灰色预测的数据是通过生成数据的gm(1,1)模型所得到的预测值的逆处理结果。(Gray theory that the behavior of the system even though the phenomenon is dim, the data is complex, but still it is ordered, there is a whole function. Gray number generation, that is, from the clutter to find out the laws. Meanwhile, the gray theory is to generate the data model, not the original data model, so gray prediction data by generating data gm (1,1) model predicted values obtained result of the inverse process.)
- 2013-09-24 00:48:16下载
- 积分：1
