canto_1978_back_of_the_envelope_1

import sympy
sympy.init_printing()
D = sympy.Symbol('D')
V = sympy.Symbol('V')
a = sympy.Symbol('alpha')
g = sympy.Symbol('gamma')
V2 = sympy.Symbol('V_2')
V1 = sympy.Symbol('V_1')
Vs = sympy.Symbol('V_*')
eqn_1 = V - 2/(g+1)*V2
eqn_2 = Vs - V1 - a*V2
eqn_3 = V - Vs - 2*(V1-Vs)/(g+1)
sympy.solve([eqn_1,eqn_2,eqn_3],[V1,V2,V])