How to not simplify symbolic expressions?

Hi all,

For a course in Dynamics of Machines I've ran into an issue with the matlab symbolic toolbox. For a simple system I derive the constraint equations expressed in symbolic coordinates in a vector; an example of the eqs is:

    sqrt((x2-x1)^2 + (y2-y1)^2)-2*sqrt(2)

This is the input code however matlab changes the equation to:

    ((x1-x2)^2 + (y1-y2)^2)^(1/2)-2*sqrt(2)

Which should give the same result, however I need the Jacobian of the contstraint vector which means signs will be incorrect in the Jacobian since matlab switched x1 and x2 around. Is there a way to prevent matlab from simplifying these symbolic expressions? Or another solution to this problem?

Thanks in advance!

[David Goodmanson]

Hi Niels,

How do you conclude that the sign of the Jacobian will be incorrect?

[Niels van Rooijen]

The jacobian takes partial derivatives, the derivative wrt x2 will now have a -1 in the chain rule differentiation instead of +1 right? I've also checked the evaluated Jacobian at the starting position to the Jacobian as calculated numerically with a simple FEM program. And indeed all values are correct however a lot of them have the wrong sign.

[David Goodmanson]

d/dx2 (x2-x1)^2 = 2*(x2-x1)
d/dx2 (x1-x2)^2 = 2*(x1-x2)*(-1) = 2*(x2-x1)

and same argument for d/dx1, so if there are sign errors I don't see how this could be the cause.

[Niels van Rooijen]

Ah shoot you're right, then I'm kinda in the dark what causes the issue.

Thanks though!

[David Goodmanson]

Of course if the roles of x1 and x2 get swapped somehow, x1 <--> x2 before you take the jacobian but the functions stay the same, then there will be a sign change. Or if the functions are swapped and x1 and x2 stay the same.

[Niels van Rooijen]

Yes but this doesn't happen it must be something else but could be anywhere else in the code.