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Homework Help: ODEs from a state vector

  1. Oct 5, 2011 #1
    I'm attempting to find a system of ODEs for a vehicle in motion that undergoes acceleration due to the gravitational pull of different bodies in space.
    It has an initial velocity, but doesn't undergo any change in acceleration due to thrust.

    This vector represents its motion.
    http://img834.imageshack.us/img834/2161/vecth.jpg [Broken]

    x and y accelerations are represented by:
    http://img805.imageshack.us/img805/3908/accel.jpg [Broken]

    I'm asked to find the first order system of ODEs and it needs to be written in the form:
    http://img411.imageshack.us/img411/3246/formh.jpg [Broken]

    I know that velocity and displacement can be found by integrating acceleration once and twice but I'm not really sure how to go about determining ODEs as a function of a state vector
    Last edited by a moderator: May 5, 2017
  2. jcsd
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