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Ballistics differential equations

  1. Mar 27, 2010 #1
    i have wandered past my math background into drag equations on bullets. i found the equation that relates acceleration and speed of the bullet. I do not know how to integrate multi-varible equations. How to i get the equation so it can be graphed on an acceleration vs time? I am thinking from there i can integrate again to velocity vs time then again to displacement vs time. I am not really interested in learning how to do this right now, since i will learn it in class later, i just need the answer to complete my program. The equation i have is
    a=(D*V^2*B*A)/(2*M)

    D=air density
    V=velocity
    B=ballistic coefficient
    A=cross sectional area
    M=mass
    Thanks for your time
     
  2. jcsd
  3. Mar 28, 2010 #2

    HallsofIvy

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    So you have
    [tex]\frac{dv}{dt}= \frac{DBA}{2M}v^2[/tex]

    That seperates as
    [tex]\frac{dv}{v^2}= \frac{DBA}{2M}dt[/tex]

    which can be integrated to
    [tex]-\frac{1}{v}= \frac{DBA}{2M}t+ C[/tex]
    where C is a constant of integration.
     
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