Higher order total derivatives

*To*: mathgroup at smc.vnet.net*Subject*: [mg81555] Higher order total derivatives*From*: janus <januswesenberg at gmail.com>*Date*: Wed, 26 Sep 2007 21:51:48 -0400 (EDT)

I am trying to avoid explicit specifying functional dependencies on time in a dynamical system. Total derivatives (Dt) seems like the right thing, but I can't get Mathematica to make the right inferences for higher order derivatives. Consider a simple example: Block[{a, v, x, t}, t /: Dt[v, t] = a; t /: Dt[x, t] = v; Dt[x, {t, 2}] ] Output: Dt[x, {t, 2}] What would I have to do to make Dt[x,{t,2}] come out as "a"? Nest[Dt[#, t] &, x, 2] gives the right answer, but I would rather not have to go this way /Janus