Help solving using ode45
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Hello everyone.
I need help solving a system of 4 first order differential equations shown below, to find the displacements x1 and y1 as well as velocities x1_dot and x2_dot. Time span is 0 to 20 seconds. Initial conditions should be zero.
x1==>displacement, x1_dot==>velocity, x2==>velocity, x2_dot==>acceleration
Where k=8500, m1=2650, m2=1830
Both Fd and Fb are functions of time and have different values for different intervals.
Fd;
Fb;
I think Fd and Fb are going to need seperate functions. Any help to solve this is much appreciated!
Thank you.
5 个评论
Bruno Luong
2018-10-3
Nadun Chandrabahu
2018-10-3
Bruno Luong
2018-10-3
编辑：Bruno Luong
2018-10-3
Sorry, I'm not going to write code for you.
However if you make an effort to write something (you might adapt the code in this thread) we can take a look.
Nadun Chandrabahu
2018-10-3
Nadun Chandrabahu
2018-10-3
Hello, I did some coding. But I'm getting the following error messages: Could you help me on how to go from here?
Below is my code,
%main script
clear all;
clc;
global x y xdot ydot t;
global k m1 m2;
k=8500;
m1=2650;
m2=1830;
%xdot(1)=x(2); %trying to write the 1st & 3rd DE's not sure if this is correct
%ydot(1)=y(2);
[t,x] = ode45('func_4wd', [0, 20], [0, 0]);
[t,y] = ode45('func_car', [0, 20], [0, 0]);
plot(t,x);
%plot(t,x);
%function (2nd DE)
function xdot = func_4wd(t,x,y)
global m1;
m1=2650;
xdot = [x(2); (DrivingF(t)/m1)-Tension(x(1),y(1))-(140/m1)*x(2)*abs(x(2))];
%function (4th DE)
function ydot = func_car(t,x,y)
global m2;
m2=1830;
ydot = [y(2); Tension(x(1),y(1))-(BrakingF(t)/m2)-((925/m2)*y(2)*abs(y(2)))];
%function for tension
function TensionOutput=Tension(X1,Y1)
if (X1-Y1)<3.5
TensionOutput=0;
else
TensionOutput=8500*(X1-Y1-3.5);
end
end
%function for driving force
function DrivingOutput = DrivingF(t)
DrivingOutput=0;
if (t>0)&&(t<=4);
DrivingOutput=(7500/197)*(150-150*cos(pi*t/4));
end
if (t>=4)&&(t<=12);
DrivingOutput=(2250000/197);
end
if (t>=12)&&(t<=16);
DrivingOutput=(7500/197)*(150-150*cos(pi*t/4));
end
end
%function for braking force
function BrakingOutput = BrakingF(t)
BrakingOutput=0;
if (t>=6)&&(t<=7);
BrakingOutput=(4000*t-24000);
end
if (t>=7)&&(t<=8);
BrakingOutput=(32000-4000*t);
end
if (t>=13)&&(t<=14);
BrakingOutput=(4000*t-52000);
end
if (t>=14)&&(t<=15);
BrakingOutput=(60000-4000*t);
end
end
采纳的回答
Bruno Luong
2018-10-3
%main script
close all
clear
k=8500;
m1=2650;
m2=1830;
[t,xy] = ode45(@(t,xy) xyder(t,xy,k,m1,m2), [0, 20], [0, 0, 0, 0]);
x = xy(:,1);
y = xy(:,3);
hold on
plot(t,x);
plot(t,y);
legend('x','y');
xlabel('t')
function xyd = xyder(t,xy,k,m1,m2)
x1 = xy(1);
x2 = xy(2);
y1 = xy(3);
y2 = xy(4);
x2d = DrivingF(t)/m1 - Tension(x1,y1,k,m1) - (140/m1)*x2*abs(x2);
y2d = Tension(x1,y1,k,m2) - BrakingF(t)/m2 -(925/m2)*y2*abs(y2);
xyd = [x2; x2d; y2; y2d];
end
%function for tension
function TensionOutput=Tension(x,y,k,m)
TensionOutput=k*(x-y-3.5)/m;
% if (x-y)<3.5 % I don't see this IF in your note
% TensionOutput=0;
% else
% TensionOutput=k*(x-y-3.5);
%end
end
%function for driving force
function DrivingOutput = DrivingF(t)
if t<4
DrivingOutput=(7500/197)*(150-150*cos(pi*t/4));
elseif t<12
DrivingOutput=(2.25e6/197);
elseif t<=16
DrivingOutput=(7500/197)*(150-150*cos(pi*t/4));
else
DrivingOutput=0;
end
end
%function for braking force
function BrakingOutput = BrakingF(t)
if (t>=6)
if t<7
BrakingOutput=(4000*t-24000);
elseif t<8
BrakingOutput=(32000-4000*t);
elseif t<14
BrakingOutput=(4000*t-52000);
elseif t<15
BrakingOutput=(60000-4000*t);
else % t>=15
BrakingOutput=0;
end
else % % t<6
BrakingOutput=0;
end
end
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