Thread Subject: Projectile Motion

Hi
I want to solve the inverse projectile motion with air resistance
problem using MATLAB, i.e. finding desired initial velocities V_x0 and
V_y0 so that the ball hits the ground at (R,0) and desired time T
(ball is thrown from (0,0) location).
I have solve the forward problem easily, i.e. finding the y_end and
t_end when the ball is thrown with some certain initial velocities. I
have defined state equiations as follows:
x1' = -K*x1*sqrt(x1^2+x2^2)
x2'= -g - K*x2*sqrt(x1^2+x2^2)
x3'= x1
x4'= x2
in which x1=V_x(t) , x2 = V_y(t) , x3 = y(t) and x4 = z(t) and g =
9.82 m/s^2 and K is friction coefficient.
I want to use Newton method to solve the problem. (Newton's method to
solve a nonlinear system F(w)=0 iterates wnew = wold - [dF/
dw(wold)^{-1}] * F(wold) and initial values for w must be given).
I would be grateful if anybody would be able to help.
Thanks in advance.

Vahid wrote:
> Hi
> I want to solve the inverse projectile motion with air resistance
> problem using MATLAB, i.e. finding desired initial velocities V_x0 and
> V_y0 so that the ball hits the ground at (R,0) and desired time T
> (ball is thrown from (0,0) location).
> I have solve the forward problem easily, i.e. finding the y_end and
> t_end when the ball is thrown with some certain initial velocities. I
> have defined state equiations as follows:
> x1' = -K*x1*sqrt(x1^2+x2^2)
> x2'= -g - K*x2*sqrt(x1^2+x2^2)
> x3'= x1
> x4'= x2
> in which x1=V_x(t) , x2 = V_y(t) , x3 = y(t) and x4 = z(t) and g =
> 9.82 m/s^2 and K is friction coefficient.
> I want to use Newton method to solve the problem. (Newton's method to
> solve a nonlinear system F(w)=0 iterates wnew = wold - [dF/
> dw(wold)^{-1}] * F(wold) and initial values for w must be given).
> I would be grateful if anybody would be able to help.
> Thanks in advance.
I'm interested in this problem,, you give the forward equation is very
nice and let me take some time to think about it.