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Question on Integrate[ F . Dt[r], ?]

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  • Subject: Question on Integrate[ F . Dt[r], ?]
  • From: pwm at (Phil W. Miller x8335 1-e138)
  • Date: Fri, 7 Feb 92 10:23:01 EST

I posted a question earlier in the week on how to make 
Dt[x y, Constants->{x}] give me x Dt[y] like the Mma
reference book says it will.  I would like to thank Jack Lee and
David Jacobson for the excellent help.  

I am trying to write a general package that will help solve Lagrange's 
equations of motion.  I am having moderate success, but there is one
major stumbling block to having a good package.  That is, what is a
good way to calculate the potential V that is the integral of the
dot product of force and virtual displacement.  Does someone know a 
general way to integrate this scalar function?  

The difficulty lies in picking the variables of integration.  For example, 
the integrand could be 
a) dV1 = x Dt[x] + y Dt[y], or
b) dV2 = x Dt[y] + y Dt[x].  

How does one devise a general scheme for integrating such expressions?
Your help is greatly appreciated.

Phil Miller

Philip Miller               The Johns Hopkins University/Applied Physics Lab
pwm at        Johns Hopkins Rd
                            Laurel, MD 20723-6099
                            (301) 953-5000 x8335 
                            FAX: (301) 953-1093

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