CODEWITHSUNDEEP
matlab
Nick
Nick

Reputation: 2980

Differentiating with MATLAB using jacobian and symbolic function

I'm running into an intriguing problem in MATLAB where I can't figure out a clean way to run the jacobian on a symbolic equation containing symbolic functions.

Let's say I have this equation for kinetic energy

kinetic energy

The variables x and phi are symbolic functions which when differentiated give diff(x(t),t) and diff(phi(t),t)

If I want to take the partial derivative of the coordinates (x_dot and phi_dot) like so

partial

I could do that if the variables were given as symbolic variables, however, in my case they are given as symbolic functions such as

diff(x(t),t)
diff(phi(t),t)

I could use the subs() function to substitute in symbolic variables but that can get messy quickly. Especially in this next step:

time

This would mean I have to re-substitute all those variables as functions so I can take the time derivative.

Any ideas on how I can easily derive these equations with the symbolic toolbox without lines and lines of code?

Upvotes: 0

Views: 304

Answers (1)

m7913d
m7913d

Reputation: 11064

I'm afraid the only thing you can do is using subs for this, but you can wrap it in a function like this:

function df = my_jacobian(f, x)
    x_ = sym('a', size(x));
    f_ = subs(f, x, x_);
    df_ = jacobian(f_, x_);
    df = subs(df_, x_, x);
end

Using this function you can calculate your jacobian similar to the example below:

syms x(t) y(t)

f = 2*diff(x(t), t) + 5*diff(y(t), t) + diff(x(t), t) * diff(y(t), t);
df = my_jacobian(f, [diff(x(t), t) diff(y(t), t)])

Upvotes: 1

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