def _solve_real_trig(f, symbol):
""" Helper to solve trigonometric equations """
f = trigsimp(f)
f = f.rewrite(exp)
f = together(f)
g, h = fraction(f)
y = Dummy('y')
g, h = g.expand(), h.expand()
g, h = g.subs(exp(I * symbol), y), h.subs(exp(I * symbol), y)
if g.has(symbol) or h.has(symbol):
return ConditionSet(symbol, Eq(f, 0), S.Reals)
solns = solveset_complex(g, y) - solveset_complex(h, y)
if isinstance(solns, FiniteSet):
return Union(
*[invert_complex(exp(I * symbol), s, symbol)[1] for s in solns])
elif solns is S.EmptySet:
return S.EmptySet
else:
return ConditionSet(symbol, Eq(f, 0), S.Reals)
def _solve_real_trig(f, symbol):
""" Helper to solve trigonometric equations """
f = trigsimp(f)
f = f.rewrite(exp)
f = together(f)
g, h = fraction(f)
y = Dummy('y')
g, h = g.expand(), h.expand()
g, h = g.subs(exp(I*symbol), y), h.subs(exp(I*symbol), y)
if g.has(symbol) or h.has(symbol):
raise NotImplementedError
solns = solveset_complex(g, y) - solveset_complex(h, y)
if isinstance(solns, FiniteSet):
return Union(*[invert_complex(exp(I*symbol), s, symbol)[1]
for s in solns])
elif solns is S.EmptySet:
return S.EmptySet
else:
raise NotImplementedError
def _solve_trig(f, symbol, domain):
""" Helper to solve trigonometric equations """
f = trigsimp(f)
f_original = f
f = f.rewrite(exp)
f = together(f)
g, h = fraction(f)
y = Dummy("y")
g, h = g.expand(), h.expand()
g, h = g.subs(exp(I * symbol), y), h.subs(exp(I * symbol), y)
if g.has(symbol) or h.has(symbol):
return ConditionSet(symbol, Eq(f, 0), S.Reals)
solns = solveset_complex(g, y) - solveset_complex(h, y)
if isinstance(solns, FiniteSet):
result = Union(*[invert_complex(exp(I * symbol), s, symbol)[1] for s in solns])
return Intersection(result, domain)
elif solns is S.EmptySet:
return S.EmptySet
else:
return ConditionSet(symbol, Eq(f_original, 0), S.Reals)
from sympy import solve, symbols, pi, sin, cos
from sympy.simplify.simplify import trigsimp
def msprint(expr):
pr = MechanicsStrPrinter()
return pr.doprint(expr)
theta = symbols('theta:3')
x = symbols('x:3')
q = symbols('q')
A = ReferenceFrame('A')
B = A.orientnew('B', 'SPACE', theta, 'xyz')
O = Point('O')
P = O.locatenew('P', x[0] * A.x + x[1] * A.y + x[2] * A.z)
p = P.pos_from(O)
# From problem, point P is on L (span(B.x)) when:
constraint_eqs = {x[0] : q*cos(theta[1])*cos(theta[2]),
x[1] : q*cos(theta[1])*sin(theta[2]),
x[2] : -q*sin(theta[1])}
# If point P is on line L then r^{P/O} will have no components in the B.y or
# B.z directions since point O is also on line L and B.x is parallel to L.
assert(trigsimp(dot(P.pos_from(O), B.y).subs(constraint_eqs)) == 0)
assert(trigsimp(dot(P.pos_from(O), B.z).subs(constraint_eqs)) == 0)
