@Guozhongzhi 2016-11-13T16:37:25.000000Z 字数 1565 阅读 670

第八次作业

计算物理 郭忠智2014301020087

【摘要】 本次作业完成了课本中3.18题的画图，为了寻找单摆的混沌现象的产生机制，我们将驱动力的大小列入考虑范围之内，观察随着驱动力的变化，单摆的运动会随之发生的变化，采用vpython画出了单摆的摆动的三维图形，以及画出 $\theta-F_D$ 的关系图，这样，我们能很清楚地看到，随着驱动力的大小变化， $\theta$ 会出现多个值，而这多个值，对应着摆的运动周期变为驱动力周期的n倍，这是混沌现象的一种形成方式。

1 背景

Problem3.18
Caculate Poincare sections for the pendulum as it undergoes the period_-doubling route to chaos.Do this for $F_D=1.4,1.44and1.465$ ,using the other parameters as given in connection with Figure3.10.

2 正文

（一）选择参数，这里我们选择的参数和第七次作业中给出的参数一致，仅让 $F_D$ 变化，观察 $\theta$ 随之变化。
（二）程序模拟
用python和vpython编写代码，运行，结果如下：

from visual import*
from math import *
#设置参数值
L = 9.8
r = 1
t = 0
dt = 0.04
g = 9.8
omiga = 0
q = 0.5
F_D = 1.4 #1.44,1.465
theta = 0.2
#画图所需元件的规格设定
scene.height, scene.width, scene.center = 1000, 1000, (0, -10, 0)
bracket = box(pos = (0,0.6*(-L-r),-2.5), length = 1, width = 0.5, 
height = 15,\
              material = materials.wood, color = color.yellow)
seat = box(pos = bracket.pos - (0,bracket.height / 2.0, 0), \
           length = 12, width = 6, height = 1, \
           material = materials.marble, color = (200,256,256))
cylinder(pos = (0,0,0.5), axis = (0,0,-3), radius = 0.3)
f = frame()
ball = sphere(frame = f, pos = (L*sin(theta), -L*cos(theta),0), \
              radius = r, material = materials.earth, color = color.white)
rope = cylinder(frame = f, pos = (0,0,0), axis = ball.pos, \
                radius = 0.2, material = materials.rough, \
                color = (0.5, 0.0, 0.5))
while True:
    rate(25)
    theta = theta + omiga * dt
    f.rotate(origin = (0,0,0),axis = (0,0,1),angle = omiga * dt)
    t = t + dt
    omiga = omiga - (math.sin(theta) + q * omiga - F_D * \
                    math.sin(2.0/3 * t)) * dt