Derive P3(x) from the Rodrigues formula, and check that P3(cos θ) satisfies the angular equation (3.60) for l = 3. Check that P3 and P1 are orthogonal by explicit integration.

Reference equation 3.60

Solution 17P

Step 1 of 4:

We need to derive the Rodrigue's formula and check out satisfies the angular acceleration equation and check out and are orthogonal by explicit integration.

The general form of Rodrigue's formula is,

Step 2 of 4:

The Rodrigue's formula for is,

The Rodrigue's formula is derived.