ODE45 to solve a 2nd order differential equation with a parameter that changes in time

Question

Tijmen 2020-11-26

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/663908-ode45-to-solve-a-2nd-order-differential-equation-with-a-parameter-that-changes-in-time

评论： Star Strider 2020-11-26

Hello! I have been working all day to solve a relatively simple second order differential equation with a parameter that has a different value for each second, but I can't get it to work. I have looked at all questions regarding this subject, but none seem to work. How do I write down my equation or ODE45 function to incorporate the time-dependence of the heave?

function [dxdt] = pitchODE(t,x,omega_5,heave,GM0,M)
dxdt_1 = x(2);
dxdt_2 = -2*0.03*omega_5*x(2)-omega_5^2*(1-(heave(t)/(2*GM0)))*x(1)+M;
dxdt = [dxdt_1; dxdt_2];
end

My heave parameter is the height of my offshore structure at each second in time.

%Defining some parameters
time = 1:1:200;     %sec
M = 1;              %N/m
GM0 = 2;            %m
omega_5 = 0.211;    %0.22 Pitch natural freq in rad/s
heave = [  ];       %a parameter with 200 values, corresponding with the 200 seconds in time
initial_x    = 0;
initial_dxdt = 0;
initial_cond = [initial_x initial_dxdt]
[t,x] = ode45(@(t,x) pitchODE(t,x,omega_5,heave,GM0,M) ,time,initial_cond)
plot(t, x(:,1))

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Answer 1

Star Strider 2020-11-26

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/663908-ode45-to-solve-a-2nd-order-differential-equation-with-a-parameter-that-changes-in-time#answer_557043

在 MATLAB Online 中打开

Interp[olate to find the appropriate values of ‘heave’ (that I call ‘heavet’ in ‘pitchODE’ ‘dxdt2’):

function [dxdt] = pitchODE(t,x,omega_5,heave,GM0,M,time)
heavet = interp1(time, heave, t);
dxdt_1 = x(2);
dxdt_2 = -2*0.03*omega_5*x(2)-omega_5^2*(1-(heavet/(2*GM0)))*x(1)+M;
dxdt = [dxdt_1; dxdt_2];
end
%Defining some parameters
time = 1:1:200;     %sec
M = 1;              %N/m
GM0 = 2;            %m
omega_5 = 0.211;    %0.22 Pitch natural freq in rad/s
heave = [  ];       %a parameter with 200 values, corresponding with the 200 seconds in time
heave = rand(1,200);
initial_x    = 0;
initial_dxdt = 0;
initial_cond = [initial_x initial_dxdt]
[t,x] = ode45(@(t,x) pitchODE(t,x,omega_5,heave,GM0,M,time) ,time,initial_cond);
plot(t, x(:,1))