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Derive P3(x) from the Rodrigues formula, and check that

Chapter 3, Problem 17P

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QUESTION:

Problem 17P

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

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QUESTION:

Problem 17P

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

ANSWER:

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,

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