Writing ODE equations for ode45 to solve;

Hi there!

I have a basic question to ask here, regarding writing the first-order equations for ode45 to solve.

Let's say I am solving Newton's 2nd law equations of motion F = ma.

In my function file, the left-hand-side of each equation will be:

1. vx (velocity of x-component)
2. vx (velocity of y-component)
3. omega (angular velocity)
4. ax (acceleration of x)
5. ay (acceleration of y)
6. omegadot (angular acceleration)

For equations 4, 5, 6, I need to use Newton's law ma = F.

Should I write ma = F as is, or do I need to isolate ax, ay, and omegadot, by dividing both sides by the mass m and the moment of inertia I, respectively? My LHS m*a is pretty lengthy, after using the product rule, chain rule, etc., so I wonder if I can just keep it as is, ma = F.

I then create an anonymous function that calls the above function, and this anonymous function is passed into ode45.

Updafe: I just tinkered with this a bit, and it does seem that I can write ma = F as is, but I have to use the double == sign, to equate values from each side, and that the single = sign is for assigning a value to a variable name. Please let me know if you have other thoughts to share.

Thanks!

Answer 1

[Torsten]

The form of the equations that can be solved by ode45 is M*y'(t) = f(t,y). So you can decide whether you choose M to be the identity matrix (that is: whether you isolate ax, ay and omegadot) or not.

[Noob]

Thanks as always, Torsten! Yes, but I found that I have to use the double equality == in my differential equations within my function file, to equate values, and that the single = sign is for assigning a value to a variable name. Please let me know if you have other thoughts. I'll accept your answer now. Thanks again!

[Walter Roberson]

You would use == only with the context of symbolic expressions. For example,

syms F(t) vx(t) vy(t) m
omega = sqrt(vx^2 + vy^2);
ax = diff(vx,t);
ay = diff(vy,t);
omega_dot = sqrt(ax^2 + ay^2);
eqn = F == m * omega_dot;
dsolve(eqn)

[Torsten]

Where do you use == ? While specifying your equations in symbolic form to prepare them for use with "ode45" via "odeToVectorField" ?

[Noob]

Oh! Nope, while I do have the Symbolic Math toolbox, I am not using it (I don't know how to use it).

I am using the single = to write ma = F in a function file.

But I am getting a warning message to use the double == sign, for equating two values.

Should I stick with the single = sign?

[Noob]

Hi Torsten / Walter,

I just tried writing ma = F as is, within my function file, but Matlab tells me it's not valid Matlab syntax.

[Torsten]

Numerical assignments only use the single "=" sign. I don't know what you try to do in your function file.

If you want to set something like

a11*y1' + a12*y2' + a13+y3' = f1

you will have to set the elements a11, a12 and a13 in the mass matrix M and the expression for f1 in your function of the right-hand side.