Solving coupled 2nd order ODEs

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OJAS POTDAR
OJAS POTDAR 2021-7-18
评论： OJAS POTDAR 2021-7-28
Hi,
I am trying to solve coupled 2nd order ODEs. When one consider quadratic air resistance, equations of motion of a projectile take the form:
mx"=-cx'(sqrt(x'^2+y'^2))
my"=-mg-cy'(sqrt(x'^2+y'^2))
where x is horizontal distance and y is vertical distance.
Can this be done in Matlab? I understand, I can reduce one second order ODE to a series of first order ODEs, but how to address coupled part i.e. x'' depends on y' and y'' depends on x'.
Thanks
  2 个评论
Torsten
Torsten 2021-7-18
x1' = x2
x2' = -c*x2*sqrt(x2^2+x4^2)/m
x3' = x4
x4' = -g -c*x4*sqrt(x2^2+x4^2)/m
where x1 is horizontal distance, x2 is horizontal velcocity, x3 is vertical distance and x4 is vertical velocity.
Now you can use one of the ODE solvers (ODE45, ODE15S).
OJAS POTDAR
OJAS POTDAR 2021-7-28
Thanks. This worked nicely:
function dydt = CatchAPass(t,y,C)
dydt = zeros(4,1);
dydt(1)= y(2);
dydt(2)= -C*y(2)*sqrt(y(2)^2+y(4)^2);
dydt(3)= y(4);
dydt(4)= -9.8-C*y(4)*sqrt(y(2)^2+y(4)^2);

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