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Angular momentum when launching projectile

  1. Feb 3, 2009 #1
    1. The problem statement, all variables and given/known data
    For a space-based platform B launching a projectile A what are the resultant inertial velocities equations and where do the launch location and projectile end up a little after launch? The platform is rotating and moving thru space and the launch mechanism imparts a fixed N*sec impulse to the projectile. The projectile is not located at the platform CG and the impulse does not act thru the platform CG.

    2. Relevant equations
    Ignore gravity, drag, and launcher friction
    Impulse acts at projectile CG
    mB = platform mass (mA for projectile)
    PB = platform initial inertial position of CG (PA for projectile)
    VB = platform initial inertial velocity of CG (VA for projectile)
    wB = platform initial inertial rotation rate about its CG (wA for projectile)
    IxxB = platform moment of inertia (IxxA for projectile)
    F = applied impulse force to projectile at time zero
    dt = time period after launch to calculate the launch and projectile location
    R = distance vector from platform CG to launch location (i.e. projectile CG at launch)

    3. The attempt at a solution
    These are vectors...
    Pre-launch:
    VA = VB since they are attached
    wA = wB since they are attached
    R = PA - PB
    After launch:
    VB(t) = VB - F / mB this is a constant
    PB(t) = PB + VB(t) t
    wB(t) = wB - F x R / IxxB this is a constant
    VA(t) = VA + F / mA + wB(t) x R this is a constant
    PA(t) = PA + VA(t) t
    R(t) = R rotated (wB(t) t)

    Launch location: PL(t) = PB(t) + R(t)
    Projectile location: PA(t)

    4. Should I be including more of the parts shown in https://www.physicsforums.com/showthread.php?t=77434
    aA = aB + wBdot x R + w x (w x R) + 2 w x VRel + aRel
     
  2. jcsd
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