Recent content by Zebx

  1. Z

    Proving Energy Conservation in a Gravitational System with Multiple Bodies

    All clear, thank you very much! :smile:
  2. Z

    Proving Energy Conservation in a Gravitational System with Multiple Bodies

    Ok, I was not sure that in this case I could exchange indeces that way. Is there some sort of "rule of thumb" which one can refer to when it comes to swap indeces? I mean, in this case I'm sure I can use ##F_{ij}## simmetry, but how can I know I will not "ruin" the general expression by changing...
  3. Z

    Proving Energy Conservation in a Gravitational System with Multiple Bodies

    Thank you for your answer. I actually already tried to write everything using ##F_{ij}## as you did, but once I reached the second equation you wrote I had problem with ##\dot{r}_j##, for instance if I used ##F_{ij} = -F_{ji}## I didn't turn also the index of ##\dot{r}_j## in ##\dot{r}_i##. So I...
  4. Z

    Proving Energy Conservation in a Gravitational System with Multiple Bodies

    Hi all. I'm trying to prove energy conservation in a (maybe) uncommon way. I know there are different ways to do this, but it is asked me to prove it this way and I'm stucked at the end of the proof. I'm considering ##N## bodies moving in a gravitational potential, such that the energy is ##E =...
  5. Z

    Equilibrium points doubt (ODE system solution)

    Perfect! thank you very much.
  6. Z

    Equilibrium points doubt (ODE system solution)

    Ok, thank you. So I suppose there are no fixed points even if I increase the number of bodies orbiting the star. I mean if I have a system of, say, 6 planets around the star still fixed in the origin. In that case I would have for every body a series of terms like ##C(\vec{x} -...
  7. Z

    Equilibrium points doubt (ODE system solution)

    Yes, I consider the star not moving at all.
  8. Z

    Equilibrium points doubt (ODE system solution)

    Hi. I'm not sure about something related to the equilibrium points (or fixed points) of a non linear ode system solution. As far as I know, to check if an equilibrium point exists, I need to put the function of my ode system equal to zero. Then once the point is found, I can use it to evaluate...
  9. Z

    Wrong solution order using Runge Kutta 4

    That seems very good! Unfortunately it is asked me to use the methods I mentioned. By the way I noticed that I forgot to mention one thing when we was talking about testing the code on simpler problmes. As I said I tested the methods on different simple problems and one of them was the linear...
  10. Z

    Wrong solution order using Runge Kutta 4

    Yes, from the Hairer book I've read that Verlet (which is the other method I'm considering cause, yes, Runge Kutta doesn't preserve the energy, but for short integration times they should provide both good results) doesn't preserve the energy exaclty, but at least errors in "positive energy" are...
  11. Z

    Wrong solution order using Runge Kutta 4

    Thank you both for the answers. I think I should have mentioned that I actually already partially tested the function as you suggested, and the method worked properly. For instance I tested it by using a single orbit, so just one body orbiting the central star, and I got the expected order. I...
  12. Z

    What can I learn about astrophysics as a physics student?

    Hi, I'm a physics student. I'm mostly interested in astrophysics and I would like to know more about it along my studies in order to understand better what to do in the future. Nice to meet you all.
  13. Z

    Wrong solution order using Runge Kutta 4

    Hi, I'm trying to simulate a 3-body problem with a star at the center of reference system and 2 body orbiting around it using Runge Kutta 4. The 2 bodies perturb each other orbits gravitationally, so my ode system is actually a coupled armonic oscillator and I evaluate the solution of both...
Back
Top