清空筛选条件
清空筛选条件

How can I integrate symbolically a coupled vector function?

1 次查看（过去 30 天）
JXT119
JXT119 2023-4-13
评论： Walter Roberson 2023-4-13
Hello,
I am trying to get a symbolic expression for the integration of a vector function arrising from a coupled differential equation, given that I want a symbolic result, I can't use ode45 and the int()m function is not working for me. My code is the following, if anyone could give me a hint about how to integrate it, it would be really appreciated.
syms v1 m u1 rho_0 beta y1 s cd g Tmax delta_u delta_v delta_y
F = [v1+delta_v;(1/m)*(Tmax*u1+(rho_0/2)*exp(-beta*y1)*(v1^2)*s*cd+rho_0*exp(-beta*y1)*v1*s*cd*delta_v-(beta/2)*rho_0*exp(-beta*y1)*(v1^2)*s*cd*delta_y)-g+(Tmax/m)*delta_u];
% F = [v1+x(2);(1/m)*(Tmax*u1+(rho_0/2)*exp(-beta*y1)*(v1^2)*s*cd+rho_0*exp(-beta*y1)*v1*s*cd*X(2)-(beta/2)*rho_0*exp(-beta*y1)*(v1^2)*s*cd*X(1))-g+(Tmax/m)*delta_u]; (Expression for ode45)
  5 个评论
显示 3更早的评论
JXT119
JXT119 2023-4-13
My solution variables are delta_v and delta_y.
y1 and v1 are nominal values around which I have linearized a non linear problem.
Walter Roberson
Walter Roberson 2023-4-13
Ran in:
It is not clear to me what is to be integrated and what the variable of integration is and what the bounds of integration are.
syms v1 m u1 rho_0 beta y1 s cd g Tmax delta_u delta_v delta_y
F = [v1+delta_v;(1/m)*(Tmax*u1+(rho_0/2)*exp(-beta*y1)*(v1^2)*s*cd+rho_0*exp(-beta*y1)*v1*s*cd*delta_v-(beta/2)*rho_0*exp(-beta*y1)*(v1^2)*s*cd*delta_y)-g+(Tmax/m)*delta_u]
F = 
syms LB UB
int(F, delta_v, LB, UB)
ans = 
int(F, delta_y, LB, UB)
ans = 
Those look valid to me.

请先登录，再进行评论。

请先登录，再回答此问题。

回答（1 个）

Torsten
Torsten 2023-4-13
移动：Torsten 2023-4-13
Ran in:
So your equations are
d(delta_v)/dt = v1 + delta_v
d(delta_y)/dt = (1/m)*(Tmax*u1+(rho_0/2)*exp(-beta*y1)*(v1^2)*s*cd+rho_0*exp(-beta*y1)*v1*s*cd*delta_v-(beta/2)*rho_0*exp(-beta*y1)*(v1^2)*s*cd*delta_y)-g+(Tmax/m)*delta_u
with all parameters except delta_v and delta_y known values ?
Then the following approach should work. Look at your equations to see how a, b, c and d have to be set.
syms t x(t) y(t)
syms a b c d real
eqn1 = diff(x,t) == a + x;
eqn2 = diff(y,t) == b*x + c*y + d
eqn2(t) = 
dsolve([eqn1,eqn2])
ans = struct with fields:
y: exp(t)*(C1 + (a*b*exp(-t))/(c - 1)) + exp(c*t)*(C2 - (exp(-c*t)*(d - (d - a*b)/c))/(c - 1)) x: -(exp(t)*(C1 + (a*b*exp(-t))/(c - 1))*(c - 1))/b

类别

在 Help Center 和 File Exchange 中查找有关 Symbolic Math Toolbox 的更多信息

标签

Community Treasure Hunt

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

Start Hunting!

Translated by