- #1

refrigerator

- 15

- 0

The author states the relationship between body rates [p q r] and Euler angle rates [φ_dot θ_dot ψ_dot]. I want to verify this but have been failing miserably...

My reasoning:

1) p, q, and r are angular rates about the body axes x

_{B}, y

_{B}, and z

_{B}.

2) φ, θ, and ψ are Euler angles about the intermediate axes x

_{2}, y

_{1}, and z

_{I}, respectively.

3) OK, so I just need to express x

_{B}, y

_{B}, and z

_{B}in terms of x

_{2}, y

_{1}, and z

_{I}, right?

4) p is trivial because x

_{B}already coincides with x

_{2}. Therefore, p = φdot.

5) When I do the same for y

_{B}, I get

y

_{B}= cosΦy

_{1}+ sinΦcosθz

_{I}+ sinΦsinθx

_{1}.

This is awfully similar to the solution given, which is

q = cosΦ * θdot + sinΦcosθ * ψdot

What am I doing wrong? I've tried to find other sources online but they all just gloss over the derivation or present the result only.

Thank you in advance... I am completely at a loss and have been thinking unproductively about this for hours.[/SUB]