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## Main Question or Discussion Point

Referring to slides 3-4 (page 2) of this link: https://www.princeton.edu/~stengel/MAE331Lecture9.pdf

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

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

3) OK, so I just need to express x

4) p is trivial because x

5) When I do the same for y

y

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]

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 gety

_{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]