Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Minimum time to stationkeeping, constant Gs

  1. Jan 22, 2009 #1
    A mechanics problem which has to have been studied, but I can't find any references on the web...

    Assume that a body in the plane is in motion at coordinates (x,0) with velocity vector (a,b). The body can be accelerated at 1 unit/sec^2 in any direction (constant G force).

    The question is how to apply the acceleration in order to bring the body to rest at (0,0) in minimum time.

    A naive solution which is easily tractable would involve applying all acceleration perpendicular to the line between the body and the origin in order to reduce the problem to 1 dimension -- first cancel all "angular momentum" and then solve the 1-D problem.

    However, there are some obvious cases where this is clearly suboptimal. For instance, the body starts at (100,0) with velocity vector (-20,1). No matter what we do, the body is going to overshoot the target by a fair bit, and the majority of the acceleration at the beginning should be directed to slowing the body down. Better to miss the target a little bit while traveling slower than to hit the target dead on at a higher speed.


    Is there a closed form solution for the desired angle at which the acceleration should be applied? The body has no "memory", so the desired acceleration at any point in time is simply a function of the position and the velocity vector.
     
  2. jcsd
  3. Jan 23, 2009 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi jbrennen ! Welcome to PF! :smile:

    Hint: As you say, we can define an angle θ which depends only on r and v … θ(r,v).

    So what is the differential equation for θ? :wink:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Minimum time to stationkeeping, constant Gs
  1. RC time constant (Replies: 2)

Loading...