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MathGroup Archive 2007

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Re: Higher order total derivatives

  • To: mathgroup at smc.vnet.net
  • Subject: [mg81583] Re: Higher order total derivatives
  • From: dh <dh at metrohm.ch>
  • Date: Fri, 28 Sep 2007 02:13:54 -0400 (EDT)
  • References: <fdf2qh$2ik$1@smc.vnet.net>


Hi Janus,

Mathematica is a pattern matcher. The pattern Dt[x, {t, 2}] does not 

appear in your definitions. Specifically, it is not interpreted as 

Dt[Dt[x,t],t]. Therefore, you must a give a rule that unravels 

Dt[x,{t,2}]. E.g.:

Unprotect[Dt];

Dt[x_,{t,0}]:=x;

Dt[x_,{t,n_}]:=Dt[Dt[x,t],{t,n-1}];

I associate the rule with Dt because t is too deeply nested for an 

association.

hope this helps, Daniel



janus wrote:

> 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

> 

> 




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