- #1
Dan_
- 2
- 0
Hello, I make the calculation of the curve rotation. Casertano(1982г.)
[itex]V^{2}=-8GR \int_{0}^{\infty}{r} \int_{0}^{\infty}{ [\frac {\partial p(r,z)} {\partial r}] \frac {K(p)-E(p)} {\sqrt{R r p}}}dzdr[/itex]
[itex]p = x - \sqrt{x^{2}-1} x=(R^{2}+u^{2}+z^{2})/(2Rr)[/itex]
Density
[itex]p(r,z) = p_{0} \exp(-r/h) [ch(z/z_{0})]^{-2}[/itex]
Derivative
[itex]\frac {\partial p(u,z)} {\partial u} = \frac {-p_{0} \exp(-r/h) [ch(z/z_{0})]^{-2}} {h}[/itex]
Original article http://articles.adsabs.harvard.edu//full/1983MNRAS.203..735C/0000737.000.html
The problem is this. Double integral should be limited. I do not know how.
[itex]V^{2}=-8GR \int_{0}^{\infty}{r} \int_{0}^{\infty}{ [\frac {\partial p(r,z)} {\partial r}] \frac {K(p)-E(p)} {\sqrt{R r p}}}dzdr[/itex]
[itex]p = x - \sqrt{x^{2}-1} x=(R^{2}+u^{2}+z^{2})/(2Rr)[/itex]
Density
[itex]p(r,z) = p_{0} \exp(-r/h) [ch(z/z_{0})]^{-2}[/itex]
Derivative
[itex]\frac {\partial p(u,z)} {\partial u} = \frac {-p_{0} \exp(-r/h) [ch(z/z_{0})]^{-2}} {h}[/itex]
Original article http://articles.adsabs.harvard.edu//full/1983MNRAS.203..735C/0000737.000.html
The problem is this. Double integral should be limited. I do not know how.