# Question:How do I analyse a numerical solution to a system of ODEs?

## Question:How do I analyse a numerical solution to a system of ODEs?

Maple 16

The system of ODEs i am trying to analyse is just a 3d model of a ball in motion with gravity and air resistence acting upon it.

restart;

with(plots):

eq1 := diff(x(t), t, t) = -k*sqrt((diff(x(t), t))^2+(diff(y(t), t))^2+(diff(z(t), t))^2)^(n-1)*(diff(x(t), t))

eq2 := diff(y(t), t, t) = k*sqrt((diff(x(t), t))^2+(diff(y(t), t))^2+(diff(z(t), t))^2)^(n-1)*(diff(y(t), t))

eq3 := diff(z(t), t, t) = -g-k*sqrt((diff(x(t), t))^2+(diff(y(t), t))^2+(diff(z(t), t))^2)^(n-1)*(diff(z(t), t))

initcondNORMAL := x(0) = 0, y(0) = 0, z(0) = 0, (D(x))(0) = cos((1/4)*Pi), (D(z))(0) = sin((1/4)*Pi), (D(y))(0) = 0

soln:=dsolve({initcondNORMAL, subs(k = 1, n = jj, g = 10, eq1), subs(k = 1, n = jj, g = 10, eq2), subs(k = 1, n = jj, g = 10, eq3)}, numeric)

What I want to do if find the highest point i.e. max(z(t)) and I want to know the t value at that point. Also the point at which it lands e.i. z(t) = 0 and the value of t at this point. Also it would be useful to find the angle of the ball tragectory with the surface at the same point. However, I can't find any way to do this in maple and I don't even know if it is possible as the system of equations I am working with can't be solved analytically for all values of n.

Any help would be greatly appreciated.
I am using maple 16.

Thanks.

David

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