Comment #30 on issue 1816 by ronan.l...@gmail.com: Adding partial
derivatives and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
There's absolutely no need here to compute diff(x', x) (whatever that
means). x and x' are separate, independent variables of the Lagrangian, and
the derivatives are taken wrt these variables, not to the physical
quantities x(t) and x'(t). To avoid confusion, write the Lagrangian as L(q,
r, t) = 1/2 * m * r**2. Then the Lagrange equation is:
d/dt(dL/dr(x, x', t)) - dL/dq(x, x', t) == 0
with dL/dr = m*r and dL/dq = 0
Hence, we get d/dt(m * x'(t)) == 0.
So this doesn't imply anything about diff(x'(t), x(t)), and as I said
before, it can be more or less anything - consider x(t) = exp(t), x(t) =
tan(t), ...
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