- #1
Korbid
- 17
- 0
I'm trying to solve numerically this multiple integral. But i don't know how to calculate it with Mathamtica or Sage software.
$$\int{e^{-(\vec{v}^2_1+\vec{v}^2_2)}e^{-E(\tau)}}d\vec{r}_1d\vec{r}_2d\vec{v}_1d\vec{v}_2$$
$$E(\tau)=\frac{k}{\tau^2}e^{-\tau/\tau_0}$$
$$\tau(\vec{r}_{12};\vec{v}_{12})=\frac{b-\sqrt{b^2-ac}}{a}$$
$$a=||\vec{v}_{12}||$$
$$b=\vec{r}_{12}\cdot\vec{v}_{12}$$
$$c=||\vec{r}_{12}|| - (2R)^2$$
Thank you!
$$\int{e^{-(\vec{v}^2_1+\vec{v}^2_2)}e^{-E(\tau)}}d\vec{r}_1d\vec{r}_2d\vec{v}_1d\vec{v}_2$$
$$E(\tau)=\frac{k}{\tau^2}e^{-\tau/\tau_0}$$
$$\tau(\vec{r}_{12};\vec{v}_{12})=\frac{b-\sqrt{b^2-ac}}{a}$$
$$a=||\vec{v}_{12}||$$
$$b=\vec{r}_{12}\cdot\vec{v}_{12}$$
$$c=||\vec{r}_{12}|| - (2R)^2$$
Thank you!