Symbolic derivative of function using diff()

For those familiar, I am writing a function to find the EOMs using the lagrangian.

I have defined all variables as syms: x(t), y(t), z(t)...

Afterward, I define eqns KE and PE as functions of x,y, and z; and L = KE - PE.

When I call diff(L,x(t)) matlab returns the correct answer, but when attempting to take a second derivative with respect to time [diff(diff(L,x(t)),t)], Matlab calls the incorrect form of diff() and yields: "Error using sym/diff, [secondary] arguments must not be symbolic." Is there a way to force this command such that it yields a result? Happy to provide specific code on request, thank you.

Answer 1

[Mahdi]

Why don't you just tell diff to take the second derivative immediately? Look under the Higher-Order Derivatives subsection for diff.

In this case, you can do:

diff(L,x(t),2) % Second derivative

[Oscar Sandoval]

Mahdi,

Second derivative is wrt a different variable - i.e. d/dt(d/dx(f(x))), in accordance with first term of lagrangian formulation of equations of motion.

[Mahdi]

Try

diff(L,x(t),t)

Also make sure that t is also defined as a symbol

syms t

[Oscar Sandoval]

Mahdi,

diff(L,x_d(t),t): 'Error using sym/diff (line 69) The second and third arguments must either be variables or a variable and a nonnegative integer specifying the number of differentiations.'

It appears to interpret 't' as t number of differentiations.

[Mahdi]

Sorry, I'm trying to understand the problem itself here. Is t a defined set of numbers? Or is it just a symbol? Can you show me the definitions of x(t) and y(t) (what you made them equal to?)?

[Oscar Sandoval]

Mahdi,

x(t) and y(t) are two of six coordinates defining position and orientation of the Center of Mass of a dynamic system. These variables are measured inputs of the system. I am attempting to solve the function symbolically to arrive at the EoMs of the system, which will then be evaluated at the measured values of x and y, amongst other inputs, in order to design a real-time controller. Are you familiar with the Euler-Lagrange equations?

[Mahdi]

Sorry for the late reply,

I am afraid that I am not. I would suggest posting the question again and adding a bit more detail. Try searching the forums because I have run into this problem into the past and found a solution online.

Answer 2

[Mischa Kim]

Check out the Euler-Lagrange tool on File Exchange.