Isotropic average of a cosine function

[peterjaybee]

Hi,

please look at the following equation.

$$\frac{3}{16}\frac{\nu_{Q}^{2}}{(1+K_{iso})\nu_{0}} \left(\frac{7}{2} \cos^{4}\theta - 3\cos^{2}\theta + \frac{5}{6}\right)$$

In the paper I am reading, this is simplified considering the isotropic average of a cosine function to

$$\frac{1}{10}\frac{\nu_{Q}^{2}}{(1+K_{iso})\nu_{0}}$$

Can someone please explain what is done? i.e. what is the isotropic average of a cosine function.

Regards

 

[mathman]

You need to supply some more detail. Isotropic usually means uniform in direction in 3 dimensions. To describe it involves two angles, like latitude and longitude.

If you are talking about uniform in 2 dimensions, then you simply need to take the average of the cos terms over a complete circle.