1.3.C.sagews

from sympy import *
from sympy import N as Num

# 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 -----------------------")
half = S(1)/2

# Derived units:
N = kg*m/s/s

FA = 6 *N
FC = FA
FB = 2 *N
FD = 5 *N

a = 3 *m
b = (4 + half) *m
c = 2 *m

# pie = 2 pi
# pie/6  = 60 deg
# pie/8 =  45 deg
# pie/12 = 30 deg
alpha = pie/6
beta  = pie/8
gamma = pie/12

print("\n--- a: -------------------------------")

cb = cos(beta)
sb = sin(beta)
cg = cos(gamma)
sg = sin(gamma)

Rx = FD * cb
Ry = -FD * sb - FB

Rx = Rx.simplify()
Ry = Ry.simplify()

R = Matrix(2,1, [Rx, Ry])
R_round=Num(R,3)
pprint(R_round/N)

print("\n--- b: -------------------------------")
# Using scalars:
MCz = a*FA + b*FB - c*FD*sb
MCz = Num(MCz/N/m,3)
pprint(MCz)

# unit vectors:
ex = Matrix(3, 1, [1, 0, 0])
eA = Matrix(3, 1, [-cg, -sg, 0])
ea = Matrix(3, 1, [-sg,  cg, 0])
eB = Matrix(3, 1, [0, -1, 0])
eD = Matrix(3, 1, [cb, -sb, 0])

rA =  a * ea
rB = -b * ex
rD =  c * ex

MA = rA.cross(FA*eA)
MB = rB.cross(FB*eB)
MD = rD.cross(FD*eD)
M = MA + MB + MD

# pick z-component:
MC = M[2].simplify()
MC = Num(MC/N/m,3)
pprint(MC)

--- User input ----------------------- --- a: ------------------------------- [3.54 ] [ ] [-5.54] --- b: ------------------------------- 19.9 19.9