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

>

>

```

• Prev by Date: Version 6 won't import Excel (Mac)
• Next by Date: Re: create a list with x,y,z coordinates
• Previous by thread: Higher order total derivatives
• Next by thread: Integrate using Assumptions