Would there be any reason that the following should not be implemented:
t = Symbol('t')
q1 = Function('q1')(t)
solve(q1 - 1, q1)
Currently, the solve function gives:
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
/home/luke/Documents/PythonDynamics/<ipython console> in <module>()
/var/lib/python-support/python2.6/sympy/solvers/solvers.pyc in
solve(f, *symbols, **flags)
73
74 if any(not s.is_Symbol for s in symbols):
---> 75 raise TypeError('not a Symbol')
76
77 if not isinstance(f, (tuple, list, set)):
TypeError: not a Symbol
In classical mechanics, the generalised coordinates are often treated
as symbols implicitly dependent upon time. Not being able to solve
for their time derivatives using solve requires tedious .subs() calls
to replace them with symbols, solve, then replace them back with
Functions.
Similarly, is there a reason we can't differentiate with respect to a
Function? For example, when using Lagrange's method for formulating
equations of motion, we need to differentiate the Lagrangian with
respect to the coordinates and with respect to the time derivatives of
the coordinates, and then take the time derivative.... Not being able
to differentiate with respect to q1.diff(t) means that one has to
create a dummy symbol for q1.diff(t), replace all occurances of it in
the Lagrangian, then take the derivative with respect to that symbol,
then back substitute to replace the symbol with the function, then
differentiate with respect to time.... a very burdensome approach
indeed.
This is what happens currently:
In [12]: diff(q3-1, q3)
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
/home/luke/Documents/PythonDynamics/<ipython console> in <module>()
/var/lib/python-support/python2.6/sympy/core/multidimensional.pyc in
wrapper(*args, **kwargs)
125 result = apply_on_element(wrapper, args, kwargs, n)
126 return result
--> 127 return f(*args, **kwargs)
128 wrapper.__doc__ = f.__doc__
129 wrapper.__name__ = f.__name__
/var/lib/python-support/python2.6/sympy/core/function.pyc in diff(f,
x, times, evaluate)
693 """
694
--> 695 return Derivative(f,x,times, **{'evaluate':evaluate})
696
697 @vectorize(0)
/var/lib/python-support/python2.6/sympy/core/function.pyc in
__new__(cls, expr, *symbols, **assumptions)
476 s = sympify(s)
477 if not isinstance(s, Symbol):
--> 478 raise ValueError('Invalid literal: %s is not a
valid variable' % s)
479 if not expr.has(s):
480 return S.Zero
ValueError: Invalid literal: q3(t) is not a valid variable
Or is there another way this can be done easily that I'm not aware of?
Thanks,
~Luke
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