On 07/12/2011 01:26 AM, sy...@googlecode.com wrote:
Comment #23 on issue 1816 by elliso...@gmail.com: Adding partial
derivatives and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
"The issue topic looks more like a simple partial derivative, as is
very commonly used in mechanic"
Yes, exactly! I have tried to say this repeatedly, and I don't know
how to say it more clearly: the functional derivatives I have
implemented are just simple partial derivatives, exactly the ones you
see in intro calculus classes when things like the chain rule are
covered:
http://mathworld.wolfram.com/ChainRule.html
You can't even write down the familiar forms of the chain rule without
accepting this basic interpretation of derivatives wrt functions. And
derivatives wrt known functions like sin/cos/exp are no different than
any others. My implementation *does* have a number of problems that I
will fix, but in my mind, there should be no confusion about what the
goal of the implementation is.
Look in http://en.wikipedia.org/wiki/Classical_field_theory under
Relativistic Fields - The Equations. You have to take the derivative
of the Lagrangian with respect to the derivatives of a vector field.
Likewise in the Lagrangian formulation of point particle mechanics you
have to take the derivative of the Lagrangian with respect to the
derivatives of the generalized coordinates \dot{q}_{i} where the q_{i}
are functions of time.
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