Having trouble with ODE45 and a System of Ordinary Differential Equations

Question

Aymeric Alejo-chaban 2019-12-4

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编辑： Stephan 2019-12-5

For a class project, I am trying to solve for an automobile’s vertical and pitching motions as a function of time. I have the equations of motion describing the vehicle and I am trying to use ODE45. However, I keep getting the error Not enough input arguments. I have tried to fiddle with each variable but I am getting nowhere. If anyone could help me it would be greatly appreciated.

Main Code:

[t,z] = ode45(@ode, [0 10], [8 0]);

plot(t,z(:,5),'-o')

plot(t,z(:,7),'-o')

title('Automobiles Vertical and Pitching Motions');

xlabel('time t');

ylabel('displacement (m)');

Function Code:

function zdot = ode(t,z)

Mv = 1500;

Jg = 1000;

Mw = 20;

kc = 200000;

kt = 350000;

l1 = 2;

l2 = 2.5;

w = 100;

zdot = zeros(1,8);

zdot(1) = z(2)

zdot(2) = (1/Mw)*(.01*cos(w*t)+kc*x(3)-(kt+kc)*x(2)-kc*l1*theta)

zdot(3) = z(4)

zdot(4) = (1/Mw)*(.01*cost(w*t)+kc*x(3)+kc*l2*theta-(kt+kc)*x(2))

zdot(5) = z(6)

zdot(6) = (1/Mv)*(kc*l1*theta+kc*x1+kc*x2-kc*l2*theta-2*kc*x3)

zdot(7) = z(8)

zdot(8) = (1/Jg)*(kc*l1*x3-kc*((l2^2)+(l1^2))*theta-kc*l1*x1-kc*l2*x3+kc*l2*x2)

%zdot = [z(2) , (1/Mw)*(.01*cos(w*t)+kc*x(3)-(kt+kc)*x(2)-kc*l1*theta) , z(4) , (1/Mw)*(.01*cost(w*t)+kc*x(3)+kc*l2*theta-(kt+kc)*x(2)) , z(6) , (1/Mv)*(kc*l1*theta+kc*x1+kc*x2-kc*l2*theta-2*kc*x3) , z(8) , (1/Jg)*(kc*l1*x3-kc*((l2^2)+(l1^2))*theta-kc*l1*x1-kc*l2*x3+kc*l2*x2)];

end

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Answer 1

Stephan 2019-12-4

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For every equation you have to input an initial condition. You have 8 but only give 2 initial conditions to ode45.

Also your function should return a column vector.

And where is x?

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Aymeric Alejo-chaban 2019-12-4

A vehicle can be modeled with the simplified model in the figure. Mv, Jv, Mw, Kc, and Kt represent the mass of the vehicle, its moment of inertia, the mass of each axle, the stiffness of each axle, and the stiffness of each tire, respectively.

Mv=1500kg, Jv=1000kgm2, Mw=20kg, kc=200kN/m, kt=350kN/m, l1=2m, l2=2.5m

Determine the following:

1.The equation of motion

2.The natural frequencies and mode shapes

3.The automobile’s vertical and pitching motions as a function of time when the road creates a displacement of 0.01cos(wt) m for each tire, where w = 100 rad/s.

Stephan 2019-12-5

编辑：Stephan 2019-12-5

Ok, can you provide the equations in a mathematical form, for example as latex?

I suspect that you have substituted x and theta by z(?) and that this makes a problem, but im not sure about this.

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Answer 2

Aymeric Alejo-chaban 2019-12-4

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All of the initial conditions should be zero so how would I go about writing that? And would the section commented out return a column vector. Finally, x and theta are what I am looking for.