3.1.D.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

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

# quantities:
quants = [
    (R, half *m),
    (w, pie/3 /s),
    (t, 1 *s)
    ]

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

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

print("--- t = 1s ---")
phi_1 = phi(w,t).subs(quants)

pprint(phi_1)

print("\n--- b: -------------------------------")
pprint("xM, yM:")
xM = R*phi(w,t)
yM = R

print("--- t ---")
pprint(Matrix([ xM, yM ]))

print("--- t = 1s ---")
xM_1 = Num(xM.subs(quants),3)
yM_1 = Num(yM.subs(quants),3)
pprint(Matrix([ xM_1, yM_1 ]))

print("\n--- c: -------------------------------")
pprint("vxM, vyM:")
vxM = diff(xM,t)
vyM = diff(yM,t)

print("--- t ---")
pprint(Matrix([ vxM, vyM ]))

print("--- t = 1s ---")
vxM_1 = Num(vxM.subs(quants),3)
vyM_1 = Num(vyM.subs(quants),3)
pprint(Matrix([ vxM_1, vyM_1 ]))

print("\n--- d: -------------------------------")
pprint("dx, dy:")
dx = - R * sin(w*t)
dy = - R * cos(w*t)

print("--- t ---")
pprint(Matrix([ dx, dy ]))

print("--- t = 1s ---")
dx_1 = Num(dx.subs(quants),3)
dy_1 = Num(dy.subs(quants),3)
pprint(Matrix([ dx_1, dy_1 ]))

print("\n--- e: -------------------------------")
pprint("xP, yP:")
xP = xM + dx
yP = yM + dy

print("--- t ---")
pprint(Matrix([ xP, yP ]))

print("--- t = 1s ---")
xP_1 = Num(xP.subs(quants),3)
yP_1 = Num(yP.subs(quants),3)
pprint(Matrix([ xP_1, yP_1 ]))

print("\n--- f: -------------------------------")
pprint("vxP, vyP:")

vxP = diff(xP,t)
vyP = diff(yP,t)
print("--- t ---")
pprint(Matrix([ vxP, vyP ]))

print("--- t = 1s ---")
vxP_1 = Num(vxP.subs(quants),3)
vyP_1 = Num(vyP.subs(quants),3)
pprint(Matrix([ vxP_1, vyP_1 ]))

print("\n--- g: -------------------------------")
pprint("axP, ayP:")

axP = diff(vxP,t)
ayP = diff(vyP,t)

print("--- t ---")
pprint(Matrix([ axP, ayP ]))

print("--- t = 1s ---")
axP_1 = Num(axP.subs(quants),3)
ayP_1 = Num(ayP.subs(quants),3)
pprint(Matrix([ axP_1, ayP_1 ]))

--- User input ----------------------- --- a: ------------------------------- phi: --- t = 1s --- 2*pi ---- 3 --- b: ------------------------------- xM, yM: --- t --- [R*omega*t] [ ] [ R ] --- t = 1s --- [1.05*m] [ ] [0.5*m ] --- c: ------------------------------- vxM, vyM: --- t --- [R*omega] [ ] [ 0 ] --- t = 1s --- [1.05*m] [------] [ s ] [ ] [ 0 ] --- d: ------------------------------- dx, dy: --- t --- [-R*sin(omega*t)] [ ] [-R*cos(omega*t)] --- t = 1s --- [-0.433*m] [ ] [ 0.25*m ] --- e: ------------------------------- xP, yP: --- t --- [R*omega*t - R*sin(omega*t)] [ ] [ -R*cos(omega*t) + R ] --- t = 1s --- [0.614*m] [ ] [0.75*m ] --- f: ------------------------------- vxP, vyP: --- t --- [-R*omega*cos(omega*t) + R*omega] [ ] [ R*omega*sin(omega*t) ] --- t = 1s --- [1.57*m ] [------ ] [ s ] [ ] [0.907*m] [-------] [ s ] --- g: ------------------------------- axP, ayP: --- t --- [ 2 ] [R*omega *sin(omega*t)] [ ] [ 2 ] [R*omega *cos(omega*t)] --- t = 1s --- [ 1.9*m ] [ ----- ] [ 2 ] [ s ] [ ] [-1.1*m ] [-------] [ 2 ] [ s ]