3.3.J.sagews

from sympy import *

# pie is better than pi
pie = 2*pi

# SI units:
m  = Symbol("m",  positive=True)
s  = Symbol("s",  positive=True)
kg = Symbol("kg", positive=True)

print("\n--- User input -----------------------")

symbolic = True
symbolic = False

if not (symbolic):
    # factors:
    MM_val, mm_val = 4,S(1)/2
    R_val = S(1)/10
    # let alpha be 30 degrees
    # pie = 2 pi
    alpha_val = pie/12
    # g = 10 m/s/s
    g_val = 10
    #
    # quantity =  factor times unit:
    MM, mm = MM_val * kg, mm_val * kg
    R = R_val * m
    alpha = alpha_val
    g = g_val * m/s/s
else:
    # quantity = symbol:
    R, MM, mm, alpha= var("R, MM, mm, alpha")
    g = var("g")

# Theta:
Tht=MM*R*R/2

# Unknowns:
# A = X''
# a = x''
# aphi = phi''
A, a, aphi, H, S = var('A, a, aphi, H, S')

print("\n--- a: -------------------------------")
# Equations to be solved:
eqs=[]
eqs.append(Eq( MM*A, MM*g*sin(alpha)-S-H ))
eqs.append(Eq( Tht*aphi, R*(H-S) ))
eqs.append(Eq( mm*a, -mm*g+S ))

print("\n--- b: -------------------------------")
eqs.append(Eq( A, R*aphi ))
eqs.append(Eq( a, 2*R*aphi ))

print("\n--- c: -------------------------------")
# Solve equations:
# set: symbolic = False
unknowns = [A, a, aphi, H, S]
sol = solve(eqs, unknowns)
pprint(sol)

print("\n--- d: -------------------------------")
# set: symbolic = True

--- User input ----------------------- --- a: ------------------------------- --- b: ------------------------------- --- c: ------------------------------- 5*m 35*kg*m 25*kg*m 5*m 25 {A: ----, H: -------, S: -------, a: ----, aphi: ----} 2 2 2 2 2 4*s 4*s 4*s 2*s 2*s --- d: -------------------------------