Solving coupled 2nd order ODEs

2021 7 18
0 个回答
更新时间：2021 7 28
6 次查看（30 天）

0 个投票

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
显示 无 隐藏 无

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);

请先登录，再进行评论。

请先登录，再回答此问题。

回答（0 个）

类别

在 帮助中心 和 File Exchange 中查找有关 Ordinary Differential Equations 的更多信息

产品

版本

R2021a

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by