3.1.J.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 -----------------------")

one = S(1)
half = S(1)/2
fourth = half*half

# symbols:
R, M, w = var("R, M, omega")
w = var("omega")
t = var("t")

# quantities:
quants = [
    (R, half *m),
    (M, one *kg),
    (w, pie /s),
    (t, fourth *s)
    ]

# Derived unit:
# Newton:
N = kg*m/s/s


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

def phi(w,t):
    """phi = omega t"""
    return w * t

print("--- t ---")
pprint(phi(w,t))

print("--- t = 1/4 s ---")
phi_4 = phi(w,t).subs(quants)
pprint(phi_4)

print("\n--- b: -------------------------------")
pprint("xP, yP:")
x = R*cos(phi(w,t))
y = R*sin(phi(w,t))

print("--- t ---")
pprint(Matrix([ x, y ]))

print("--- t = 1/4 s ---")
x_4 = Num(x.subs(quants),3)
y_4 = Num(y.subs(quants),3)
pprint(Matrix([ x_4, y_4 ]))


print("\n--- c: -------------------------------")
pprint("vxP, vyP:")
vx = diff(x,t)
vy = diff(y,t)

print("--- t ---")
pprint(Matrix([ vx, vy ]))

print("--- t = 1/4 s ---")
vx_4 = Num(vx.subs(quants),3)
vy_4 = Num(vy.subs(quants),3)
pprint(Matrix([ vx_4, vy_4 ]))

print("\n--- d: -------------------------------")
pprint("axP, ayP:")
ax = diff(vx,t)
ay = diff(vy,t)

print("--- t ---")
pprint(Matrix([ ax, ay ]))

print("--- t = 1/4 s ---")
ax_4 = Num(ax.subs(quants),3)
ay_4 = Num(ay.subs(quants),3)
pprint(Matrix([ ax_4, ay_4 ]))

print("\n--- e: -------------------------------")
pprint("vxP, vyP:")
vr = 0
vp = R*w

print("--- t ---")
pprint(Matrix([ vr, vp ]))

print("--- t = 1/4 s ---")
vr_4 = Num(0,3)
vp_4 = Num(vp.subs(quants),3)
pprint(Matrix([ vr_4, vp_4 ]))

print("\n--- f: -------------------------------")
pprint("axP, ayP:")
ar = - R*w*w
ap = 0

print("--- t ---")
pprint(Matrix([ ar, ap ]))

print("--- t = 1/4 s ---")
ar_4 = Num(ar.subs(quants),3)
ap_4 = Num(0,3)
pprint(Matrix([ ar_4, ap_4 ]))

print("\n--- g: -------------------------------")
pprint("S:")
S = M * R *w*w
pprint(S)
S_4 = S.subs(quants)

# S in Newton:
pprint(Num(S_4/N,3))

--- User input ----------------------- --- a: ------------------------------- phi: --- t --- omega*t --- t = 1/4 s --- pi -- 2 --- b: ------------------------------- xP, yP: --- t --- [R*cos(omega*t)] [ ] [R*sin(omega*t)] --- t = 1/4 s --- [ 0 ] [ ] [0.5*m] --- c: ------------------------------- vxP, vyP: --- t --- [-R*omega*sin(omega*t)] [ ] [R*omega*cos(omega*t) ] --- t = 1/4 s --- [-3.14*m ] [--------] [ s ] [ ] [ 0 ] --- d: ------------------------------- axP, ayP: --- t --- [ 2 ] [-R*omega *cos(omega*t)] [ ] [ 2 ] [-R*omega *sin(omega*t)] --- t = 1/4 s --- [ 0 ] [ ] [-19.7*m ] [--------] [ 2 ] [ s ] --- e: ------------------------------- vxP, vyP: --- t --- [ 0 ] [ ] [R*omega] --- t = 1/4 s --- [ 0 ] [ ] [3.14*m] [------] [ s ] --- f: ------------------------------- axP, ayP: --- t --- [ 2] [-R*omega ] [ ] [ 0 ] --- t = 1/4 s --- [-19.7*m ] [--------] [ 2 ] [ s ] [ ] [ 0 ] --- g: ------------------------------- S: 2 M*R*omega 19.7