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Magnitudes of Velocity and Acceleration

  1. Dec 10, 2014 #1
    1. The problem statement, all variables and given/known data
    I need to determine the magnitude of velocity and acceleration for an aircraft moving away from a fixed position (for example a radar station). I need to calculate the magnitude of velocity and acceleration for each time step.

    The following table of information is given
    prob.jpg


    2. Relevant equations
    The magnitude of velocity is given as
    [tex]\sqrt{(\frac{dr}{dt})^2+(r\frac{d\theta}{dt})^2}[/tex]

    And acceleration
    [tex][\frac{d^2r}{dt^2}-r(\frac{d\theta}{dt})^2]^2+[r\frac{d^2\theta}{dt^2}+2\frac{dr}{dt}\frac{d\theta}{dt}]^2[/tex]

    3.0 Attempt
    I am currently in the process of programming this into FORTRAN to get results but I am struggling to work out how to calculate. I am just hoping someone can point me in the right direction. I know I need to calculate the first and second derivatives but the fact I need to take an angle into account is confusing me somewhat. Also to add, how can I calculate a magnitude of velocity for time 0?
     
  2. jcsd
  3. Dec 10, 2014 #2

    DrClaude

    User Avatar

    Staff: Mentor

    The best is to use the finite difference method.


    There are different approaches you can take. The simplest is to used a forward difference, which uses only information at the current and later times.
     
  4. Dec 10, 2014 #3
    Thanks for that, I will try and implement into my program!
     
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