How can i solve this?

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B A 2015-1-2

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评论： B A 2015-1-2

How can I solved this....:( Please help ... The motion of two bodies under mutual gravitational attraction is described by the following equations derived from Newton's law of Motion.

     x’’(t) = - α^2*x(t)/R(t),
     y’’(t) = - α^2*y(t)/R(t),

where x(t) and y(t) denote the position of one body in a coordinate system with the origin fixed in the other body,R(t) = (x^2(t)+ y^2(t))^3/2 , and α is a constant.

      x(0)=1-β , x'(0)=0
      y(0)=0, y'(0)=α sqr((1+β)/(1-β))

Here β is a constant, 0≤β<1. The orbit is then an ellipse with eccentricity β and one focus at the origin. Choose α = π/4 and β =0.9.

Write a program based on the classical Runge-Kutta 4-th -ordered method in Matlab. Test your code with a fixed step size h on the problem above.For the set of printout point t(k)= k/2 , k=0,....24 print out the position and for all the steps taken plot the position (x(t), y(t)), velocity (x'(t),y'(t))and acceleration(x"(t),y"(t)). Verify the theoretical dependence of accuracy on the step size , h .Note then the solution is periodic , with the period P=8.Observe how close the bodies come to each other.