A custom subs for use on expressions derived in physics.mechanics.
Traverses the expression tree once, performing the subs found in sub_dicts. Terms inside Derivative expressions are ignored:
>>> from sympy.physics.mechanics import dynamicsymbols, msubs
>>> x = dynamicsymbols('x')
>>> msubs(x.diff() + x, {x: 1})
Derivative(x(t), t) + 1
Note that sub_dicts can be a single dictionary, or several dictionaries:
>>> x, y, z = dynamicsymbols('x, y, z')
>>> sub1 = {x: 1, y: 2}
>>> sub2 = {z: 3, x.diff(): 4}
>>> msubs(x.diff() + x + y + z, sub1, sub2)
10
If smart=True (default False), also checks for conditions that may result in nan, but if simplified would yield a valid expression. For example:
>>> from sympy import sin, tan
>>> (sin(x)/tan(x)).subs(x, 0)
nan
>>> msubs(sin(x)/tan(x), {x: 0}, smart=True)
1
It does this by first replacing all tan with sin/cos. Then each node is traversed. If the node is a fraction, subs is first evaluated on the denominator. If this results in 0, simplification of the entire fraction is attempted. Using this selective simplification, only subexpressions that result in 1/0 are targeted, resulting in faster performance.
Find all dynamicsymbols in expression.
>>> from sympy.physics.mechanics import dynamicsymbols, find_dynamicsymbols
>>> x, y = dynamicsymbols('x, y')
>>> expr = x + x.diff()*y
>>> find_dynamicsymbols(expr)
set([x(t), y(t), Derivative(x(t), t)])
If the optional exclude kwarg is used, only dynamicsymbols not in the iterable exclude are returned.
>>> find_dynamicsymbols(expr, [x, y])
set([Derivative(x(t), t)])