How to collect specific terms from an expression?

Hello.

I have an expression like:

syms theta1 syms theta2 syms Dtheta1 syms Dtheta2 syms DDtheta1 syms DDtheta 2 syms g

t2 = 3*sin(theta2)*Dtheta1^2 + 3*DDtheta1 + 3*DDtheta2 + 3*g*cos(theta1+theta2) + 3*DDtheta1*cos(theta2)

I would like to be able to extract component terms from t2 (torque). For example, M21 would be the term that only multiplies DDtheta1. M22 would be the term that only multiplies DDtheta2. G would be the term that only multiplies g. And so on.

I tried to use the function collect, but I could not give values for the other variables to make them zero.

I was trying M21 = collect(t2, [DDtheta1 = 1, DDtheta2 = 0 , Dtheta1 = 0, Dtheta2 = 0, g = 0]) but MATLAB tells me it is wrong.

Does anyone know how I could do this? Thanks!

Answer 1

[Star Strider]

I’m not certain I understand.

Try this:

syms theta1 theta2 Dtheta1 Dtheta2 DDtheta1 DDtheta2 g M21 M22 G

% t2 = 3*sin(theta2)*Dtheta1^2 + 3*DDtheta1 + 3*DDtheta2 + 3*g*cos(theta1+theta2) + 3*DDtheta1*cos(theta2)

t2 = 3*sin(theta2)*Dtheta1^2 + M21*DDtheta1 + M22*DDtheta2 + G*g*cos(theta1+theta2) + 3*DDtheta1*cos(theta2)

M21 = solve(t2, M21)

M22 = solve(t2, M22)

G = solve(t2, G)

[Yurik Coelho]

I would like to get smaller parts of t2 (total torque) to be able to plot them individually, I am doing a dynamic modelling of a robot, so every term is a specific torque that I have to get and plot. For example:

M21 would be the term that multiplies DDtheta1 in t2, so:

M21 = 3 + 3*cos(theta2)

M22 would be the term that multiplies DDtheta2 in t2,so:

M22 = 3

G would be the term that multiplies g in t2, so:

G = 3*cos(theta1+theta2)

but t2 is a small expression, so I can do that manually. But I will get huge expressions that it will become very difficult to do that.

[Star Strider]

In that situation, set up your equation as:

syms ... M21 M22 G 

M21 = 3 + 3*cos(theta2)

M22 = 3

G = 3*cos(theta1+theta2)

then:

t2 = M21*DDtheta2 + M22*DDtheta2 + G*g ...

This gives you access to the coefficient expressions as well as t2.

Would that do what you want?

[Yurik Coelho]

No, because I don't know M21, M22 and G. I just know t2. Suppose t2 is a huge expression that has 50 lines in matlab. How would you get just the component that multiplies DDtheta1? Suppose that you don't even look at t2 expression, you just write something that will give you this component.

There is a Maple code that do that. I am using it to get the components. See:

I would like to know if MATLAB can do the same as Maple did there. But if it doesn't exist something like this in MATLAB, it's fine. I will just use Maple instead.

[Star Strider]

If you’re setting all the others to zero to get the one you’re interested in, you can certainly do that with the Symbolic Math Toolbox:

syms theta1 theta2 Dtheta1 Dtheta2 DDtheta1 DDtheta2 g M21 M22 G

t2 = 3*sin(theta2)*Dtheta1^2 + 3*DDtheta1 + 3*DDtheta2 + 3*g*cos(theta1+theta2) + 3*DDtheta1*cos(theta2)

G = subs(t2, {Dtheta1, DDtheta1, DDtheta2, DDtheta1}, {0, 0, 0, 0})

produces:

G =

      3*g*cos(theta1 + theta2)

[Yurik Coelho]

That was exactly what I was looking for! Thank you!

[Star Strider]

My pleasure!