DumbbellUtilities.py

import numpy
import sys
 
def getLagrangianMultiplicatorRatioFromWeissenbergNumber(Wi):
    if Wi == 0:
        return 1
 
    coefficients = [1, -1, 0, -Wi * Wi / 6.0] #see Kowalik and Winkler's paper
 
    roots = numpy.roots(coefficients)
 
    if len(roots) != 3:
        raise RuntimeError("Unexpected number of roots in " + sys._getframe().f_code.co_name)
 
    if not numpy.array_equal(numpy.isreal(roots), [True, False, False]):
        raise RuntimeError("Unexpected types of roots in " + sys._getframe().f_code.co_name)
 
    return roots[0].real