I am trying use shooter's method to solve a second order differential equation

Question

adam puchalski 2022-7-14

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1760145-i-am-trying-use-shooter-s-method-to-solve-a-second-order-differential-equation

评论： James Tursa 2022-7-14

I am trying to loop and find the best value for curvature (im trying to find this) and will later put this in, but essentially I am trying to use shooters method to solve this: D^2y/dx^2 = F*sin(t)/(E*I)

i am using two first order diff eqs and solving via the boundary conditions.

this is as far as i got, my four equations are in the fun line:

d(theta)/dt = u

du/dt = Fsin(t)/EI

dx/dt = sin(t)

dy/dt = cos(t)

i am new to matlab, but i am interested in plotting the results of sin and cos. when i plot sin and cos so (shooterY and shooterX) is it not factoring in my equation at all? instead just plotting sin as a function of cos?

I just want to make sure I am doing this correctly with the ODE34 function

%variables
F = .024; %kg
E = 10^6; %mPa
I = 6.1*10^-9; %kg m^2
L = .01; %m
        
        %for loop to cycle through and find best one
        for curvature = 10^-7:10^-6:1*10^-6
                fun = @(t, s) [s(2); F*sin(t)/(E*I); sin(t); cos(t)];%The actual function
                tspan = [0 L]; %time to make sure goes to the lenght of the rod
                Y0 = [0 curvature 0 0];%guesses that are beign cycled
                [x,y] = ode45(fun, tspan, Y0);%fucntion to do the integrals
                dt = y(1:end,1); du = y(1:end,2); shooterY = y(1:end,3); shooterX = y(1:end,4); %extracting the data
                
%                 if sin(t)/(EI) == 0
%                     break
%                 end
                   %break when moment at end is 0
        end
        