$$\ddot{\vec{r}}_k=\sum_{i=1,i != k}^{n} Gm_i\frac{\vec{r}_i-\vec{r}_k}{|\vec{r}_i-\vec{r}_k|^3}$$

The Three Body Problem and its Classical Integration

1、A、B为两定点，可看作有刚性杆连接；
2、AC为动力杆，绕点A转动；
3、BD为从动杆，CD为连杆。

1、CD=AB=$\sqrt{2}$；
2、AC=BD=1。
3、E是CD中点

The New Calculation Of Lagrangian Point 4,5

The New Calculation Of Lagrangian Point 1,2,3

L2_rendering

$$\ddot{\vec{r}}_k=\sum_{i=1,i != k}^{n} Gm_i\frac{\vec{r}_i-\vec{r}_k}{|\vec{r}_i-\vec{r}_k|^3}\tag{19}$$

储备

$$\frac{2}{\tan 2A}=\frac{1}{\tan A}-\tan A$$
$$\frac{2}{\sin 2A}=\frac{1}{\tan A}+\tan A$$
$$\cos(3A)=4\cos^3 A-3\cos A$$