exercise 09

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背景

As we have known,Hyperion has an unusual shape,leading to its different behavior.Hyperion is shaped more like an egg and its orbit is choatic.
We let $\theta$ be the angle that the rod makes with the x axis and define the associated angular velocity $\omega=d\theta/dt$.The center of the mass of the object is $x_c$ and $y_c$.
After some algebra,we can obtain:

$$\frac{d\omega}{dt}\approx-\frac{3GM_{Sat}}{r_c^5}(x_csin{\theta}-y_ccos{\theta})(x_ccos{\theta}+y_csin{\theta})$$ We can obtain $\omega$ by using $d\theta/dt=\omega$

正文

for circular and elliptical orbit,reset $\theta$


$\Delta{\theta}$ and $\Delta{\omega}$ for circular and elliptical orbit reset $\theta$


not keep $\theta$ in range $-\pi$ to $\pi$ for circular and elliptical orbit

change the initial conditions
$\Delta{\theta}=0.01$,change the initial velocity

$\Delta{\theta}=0.05$,change the initial velocity

代码

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