1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Body rates from Euler angles...

  1. May 23, 2016 #1
    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 xB, yB, and zB.
    2) φ, θ, and ψ are Euler angles about the intermediate axes x2, y1, and zI, respectively.

    3) OK, so I just need to express xB, yB, and zB in terms of x2, y1, and zI, right?

    4) p is trivial because xB already coincides with x2. Therefore, p = φdot.
    5) When I do the same for yB, I get
    yB = cosΦy1 + sinΦcosθzI + sinΦsinθx1.

    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]
     
  2. jcsd
  3. May 23, 2016 #2
    I just saw the stickied thread about posting homework-type questions here... I hope this doesn't qualify as a homework-type question. Although it does involve debugging my thought process, it is also a conceptual question about why my reasoning is wrong. If this counts as a homework-type question, my apologies.
     
  4. May 24, 2016 #3

    FactChecker

    User Avatar
    Science Advisor
    Gold Member

    No. x,y,z refer to positions in the axis systems, not rotation rates. If any x,y,z is in your answer, that is wrong. You want to express p, q, r in terms of φ, θ, ψ, φdot, θdot, and ψdot.
     
  5. May 24, 2016 #4

    vanhees71

    User Avatar
    Science Advisor
    2016 Award

    You can derive the angular momentum vector from
    $$\omega_j=1/2 \epsilon_{jkl} (D^{-1} \dot{D})_{kl}=1/2 \epsilon_{jkl} (D^{\mathrm{T}}\dot{D})_{kl},$$
    where ##D=D(\varphi,\vartheta,\psi)## is the SO(3) matrix in terms of Euler angles to be read as function of time, ##t##.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted