In Response To 'Re: Re: Symbolic Computation'
Another way is to use the ordinary function notation r[t]. Then r'[t] or D[r[t],t} will represent the derivative and can be used to set up differential equations for DSolve or NDSolve.
Or you can use r[t,x,y,phi] if you wish. Watch out, though: In this case the derivative operator D[..] yields partial derivatives. If you want to treat everything as a function of time, write r[t, x[t], y[t], phi[t]]. Try D[r[t, x[t], y[t], phi[t]], t] and see if you can parse the notation. (If confusing, try the partial derivative D[r[t, x, y, phi], x] without all the t's. What you will see is the output form of Derivative[0, 1, 0, 0][r][t, x, y, phi].)
In this form you probably ought not to set t=2 for instance. Then r[t] is the same as r. You'll have to Unset or Clear t to get t back as a variable. The same goes for r, x, y, and phi.