Re: differentiation of cross products
- To: mathgroup at smc.vnet.net
- Subject: [mg16495] Re: [mg16419] differentiation of cross products
- From: "Kevin J. McCann" <kevinmccann at Home.com>
- Date: Tue, 16 Mar 1999 03:59:46 -0500
- Sender: owner-wri-mathgroup at wolfram.com
You need to have g[t] and h[t] be vectors:
g[t_]={gx[t],gy[t],gz[t]};
h[t_]={hx[t],hy[t],hz[t]};
before you can take the CrossProduct. The derivative then works, but does
not give you a
nice simple form.
Kevin
-----Original Message-----
From: Issac Trotts <trotts at ucdavis.edu>
To: mathgroup at smc.vnet.net
Subject: [mg16495] [mg16419] differentiation of cross products
>Can anyone tell me how to differentiate the cross product
>of two vector-valued functions in Mathematica?
>The input
>
>D[Cross[g[t],h[t]],t]
>
>results in the output
>
>h'[t] Cross^(0,1)[g[t], h[t]] + g'[t] Cross^(1,0)[g[t], h[t]]
>
>which is not correct. The correct answer would be
>
>Cross[g'[t], h[t]] + Cross[g[t], h'[t]]
>
>I also tried
>
>(Cross[g[#],h[#]]&)'
>
>which gave me the following incorrect output:
>
>Cross^(1,0)[g[#1], h[#1]] g'[#1] + Cross^(0,1)[g[#1], h[#1]] h'[#1] &
>
>Please tell me if you know of a good way to deal with
>this problem.
>
>Thanks,
>Issac Trotts
>
>P.S.: Please send your response to trotts at ucdavis.edu .
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