1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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 Explorer-1 tipped over, but Euler equation doesn't agree

  1. Mar 9, 2016 #1
    [tex]\dot{\boldsymbol{H}} = \dot{\omega} + \boldsymbol{\omega}\times\boldsymbol H[/tex]
    Suppose body's got an impulse and 's started to rotate about its principle axis, say z, No more external moment from this time.
    So, Euler equations become
    [tex]0 = I_{xx}\dot{\omega}_x − (I_{yy} − I_{zz}) \omega_y \omega_z[/tex]
    [tex]0 = I_{xx}\dot{\omega}_y − (I_{yy} − I_{zz}) \omega_z \omega_x[/tex]
    [tex]0 = I_{xx}\dot{\omega}_z − (I_{yy} − I_{zz}) \omega_x \omega_y[/tex]

    Suppose small rotation was imparted along another axis z or y in such a way that [itex]\omega_z >> \omega_x, \omega_z >> \omega_y.[/itex]

    From differential equation we can get, we conclude that a body rotating about an axis where the moment of inertia is intermediate between the other two inertias, is unstable.

    But, Explorer-1 was rotation about its longest axis - the one with smallest inertia, and tipped over due to internal forces, so rotation about axis with smallest inertia moment is unstable. Doesn't that contradict to the previous result?
    Last edited: Mar 9, 2016
  2. jcsd
  3. Mar 14, 2016 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Threads - Explorer tipped Euler Date
I Can a bicycle be tipped over by only applying rear brake? Jan 16, 2018
Insights Exploring the Spectral Paradox - Comments May 1, 2017
I Computer exploration of fundemental constants Aug 12, 2016
Insights Secondary Forces Explored - Comments Feb 6, 2016