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Derive the terrestrial equation of motion in the body-fixed frame

  1. Jan 24, 2014 #1
    1. The problem statement, all variables and given/known data

    Assume that the center of mass of the earth moves with approximately constant velocity with respect to the fixed stars, and that [itex]\mathbf{\omega}[/itex], the angular velocity of the earth, is constant. Rederive the terrestrial equations of motion
    [tex]\mathbf{F}'+m\mathbf{g}[/tex][tex]m\ddot{\mathbf{r}}-2m\mathbf{\omega}\times\dot{\mathbf{r}}[/tex]
    By writing Newton's laws in a body-fixed frame with the origin at the surface of the earth.

    2. Relevant equations

    For a particle with coordinates [itex]\mathbf{r}_0[/itex] in the inertial frame and [itex]\mathbf{r}[/itex] in the body-fixed frame, where the origin of the body fixed frame is at the instantaneous point [itex]\mathbf{a}[/itex] with respect to the inertial frame.
    [tex]\mathbf{r}_0 = \mathbf{a}+\mathbf{r}[/tex]

    3. The attempt at a solution

    I'm pretty confused on where to start here. I know that in the inertial frame [itex]\mathbf{F}=m\mathbf{A}[/itex]. Could anyone help get me started, or point me towards some literature on this?
     
  2. jcsd
  3. Jan 24, 2014 #2
    wait I think I just arrived at the first equation.
     
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