1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I MATLAB - Motion of a body around a central one

  1. Nov 30, 2016 #1

    MMS

    User Avatar

    Hello everyone,

    I've written a code using ode45 which describes the motion of a body m around a central one M (e.g a satellite around earth). I've done it with initial values that set the trajectory of the particle to be elliptic.

    Clearly, energy and angular momentum need be conserved in this and so I get. However, I'm looking to reduce the error as much as possible and get a more accurate solution.

    For the energy, I've managed to get a really small one using the relative and absolute tolerance. For example, for some parameters of RelTol and AbsTol, the relative error can reach a maximum value of about ~1e-8% only for 50 periods. However, the relative error in angular momentum doesn't seem to be affected by whatever I set the RelTol and AbsTol to be and the maximum value that it reaches (it is periodic, see the graph below) is constant at 11.36%.

    I've already tried playing with the step size as well and it doesn't seem to affect it.

    You can see two images below that describe the energy and angular momentum in 50 periods. The y axis describes the relative error (not in percentage) in each parameter and the x axis describes the number of periods (50 in this case).

    Does anyone have any suggestion as to how to control and diminish the relative error in angular momentum?

    Thanks in advance.

    ptp5dPz.jpg
    olFVQ7A.jpg
     
  2. jcsd
  3. Dec 1, 2016 #2
    I think that function uses the Runge-Kutta Method. The Runge-Kutta method is prone to energy error divergence at a long timescale when the true orbit should be periodic. The Verlet method allows bounded error in energy for periodic orbits. I am not sure if using Verlet instead would lead to better angular momentum error. I am not sure about the issue you are having with angular momentum error or how to improve it except smaller step size.

    I am also wondering about ode solvers which might be able to enforce constraints like conserved energy somehow.
     
  4. Dec 2, 2016 #3

    MMS

    User Avatar

    It does use the Runge-Kutta method and you can see from the results that the error in energy is very small so I don't really have a problem with that.
    However, the angular momentum stays the same regardless of the step size I take...
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: MATLAB - Motion of a body around a central one
  1. Bodies in motion… (Replies: 3)

  2. Motion of a body (Replies: 3)

Loading...