Differentiating Cross
- To: mathgroup at smc.vnet.net
- Subject: [mg66238] Differentiating Cross
- From: "Vladimir" <vladimir347 at yahoo.com>
- Date: Fri, 5 May 2006 05:02:27 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Hello!
We have a handy default rule for Dot:
In[]:= Dt[a . b, t]
Out[]= a . Dt[b, t] + Dt[a, t] . b
So I'd like to have a similar behavior for Cross,
but it looks like chain rule is used instead:
In[]:= Dt[Cross[a, b], t]
Out[]= Dt[b, t]*Derivative[0, 1][Cross][a, b] +
Dt[a, t]*Derivative[1, 0][Cross][a, b]
So I defined required transformation:
In[]:= Unprotect[Dt];
Dt[Cross[a_, b_], t_] := Cross[a, Dt[b, t]] + Cross[Dt[a, t], b];
which works for just Dt[Cross[a, b], t],
but it still doesn't work when Cross is a part
of expression like Dt[Cross[a, b] + c, t] etc.
What am I doing wrong?
--
Vladimir