'Helper method for _connect_to_cartesian. It checks if
set of transformation equations create orthogonal curvilinear
coordinate system
Parameters
equations : tuple
Tuple of transformation equations'

def _check_orthogonality(self):

    eq = self._transformation_equations()
    v1 = Matrix([diff(eq[0], self.x), diff(eq[1], self.x), diff(eq[2], self.x)])
    v2 = Matrix([diff(eq[0], self.y), diff(eq[1], self.y), diff(eq[2], self.y)])
    v3 = Matrix([diff(eq[0], self.z), diff(eq[1], self.z), diff(eq[2], self.z)])
    if any(((simplify(((i[0] + i[1]) + i[2])) == 0) for i in (v1, v2, v3))):
        return False
    elif ((simplify(v1.dot(v2)) == 0) and (simplify(v2.dot(v3)) == 0) and (simplify(v3.dot(v1)) == 0)):
        return True
    else:
        return False
