# Example 16.2
MKS
ra = 0.15 m
rb = 0.4 m
a = 2 rad/s^2
qb = 2 * pi() rad
qa = qb * rb / ra
oma = sqrt(2 * a * qa)
omb = oma * ra / rb
ab = a * ra / rb
vp = omb * rb
apt = ab * rb
apn = omb^2 * rb
ap = sqrt(apt^2 + apn^2)

# Example 16.5
MKS(deg)
v = 0.5 m/s
q = 30 deg
x2 = 2m
x1 = 1 m
ss = sqrt(x2^2 + x1^2 - 2 * x1 * x2 * cos(q))
om = ss * v / (2 * sin(q))
a = (0.5^2 - 2 * cos(q) * (0.620)^2) / (2 * sin(q))

# Example 16.6
MKS(deg)
q = 45 deg
r = PolarVec(0.2 m, q)
va[2] = -2 m/s
BEGIN
  om[3] = 1 rad/s
  vb = va + cross(om, r)
END
solve(vb[2], om[3])

# Example 16.7
FPS(deg)
vb[1] = 2 ft/s
om[3] = -15 rad/s
r = [-0.5, 0.5] ft
va = vb + cross(om, r)
Mag(va)
PolarAngle(va)

# Example 16.8
MKS(deg)
vc[2] = -2 m/s
r = [0.2, -0.2] m
BEGIN
om[3] = 1 rad/s
vb = vc + cross(om, r)
END
solve(vb[2], om[3])

# Example 16.9
MKS(deg)
om[3] = -30 rad/s
r = PolarVec(0.2 m, 60 deg)
vb = cross(om, r)
rcb[1] = 0.2 m
BEGIN
ombc[3] = 1 rad/s
vc = vb + cross(ombc, rcb)
END
solve(vc[2], ombc[3])
rc[2] = -0.1 m
BEGIN
omd[3] = 1 rad/s
e = vc - cross(omd, rc)
END
solve(e[1], omd[3])

# Example 16.11
MKS(deg)
q = 45 deg
x = 0.4 m
rb = x * tan(q)
rd = rb / cos(q)
vd = 3 m/s
ombd = vd / rd
vb = ombd * x
omab = vb / rb

# Example 16.12
MKS
vd = 0.4 m/s
ve = 0.25 m/s
r = 0.125 m
BEGIN
x = 1 m
om = 1 rad/s
e1 = vd - om * x
e2 = ve - om * (2 * r - x)
END
solve(e1,e2,x,om)
rc = x - r
vc = om * rc

# Example 16.13
MKS
r[1] = 10 m
om = 0.283 rad/s
q = 45 deg
BEGIN
   a = 1 m/s^2
   ab = PolarVec(a, q)
   aa = PolarVec(3 m/s^2, q)
   alp[3] = 1 rad/s^2
   e = ab - (aa + cross(alp, r) - om^2 * r)
END
solve(e[1], e[2], a, alp[3])

# Example 16.15
alph[3] = 4 rad/s^2
rbo[1] = 0.5 m
om = 6 rad/s
a0[1] = -2 m/s^2
ab = a0 + cross(alph, rbo) - om^2 * rbo
rao[2] = 0.5 m
aa = a0 + cross(alph, rao) - om^2 * rao

# Example 16.16
FPS(deg)
om = 3 rad/s
alp[3] = -4 rad/s^2
r = 0.5 ft
ag[2] = -2 ft/s^2
rbg[2] = 0.75 ft
ab = ag + cross(alp , rbg) - om^2 * rbg
mag(ab)
PolarAngle(ab)

# Example 16.17
BEGIN
   alp_ab[3] = 1 rad/s^2
   rb[2] = -0.2 m
   omab = 10 rad/s
   ab = cross(alp_ab, rb) - omab^2 * rb
   ac[2] = -1 m/s^2
   rbc = [0.2, -0.2] m
   omcb = 10 rad/s
   alp_cb[3] = 1 rad/s^2
   e = ab - (ac + cross(alp_cb, rbc) - omcb^2 * rbc)
END
solve(e[1], e[2], alp_cb[3], alp_ab[3])

# Example 16.18
FPS(deg)
q = 45 deg
rb = 0.25 ft * [-sin(q), cos(q)]
q2 = 13.6 deg
rcb = 0.75 ft * [sin(q2), cos(q2)]
alp_ab[3] = -20 rad/s^2
omab = 10 rad/s
ab = cross(alp_ab, rb) - omab^2 * rb
BEGIN
alp_bc[3] = 1 rad/s^2
ombc = 2.43 rad/s
ac = ab + cross(alp_bc, rcb) - ombc^2 * rcb
END
solve(ac[1], alp_bc[3])

# Example 16.19
MKS(deg)
om[3] = -3 rad/s
omdot[3] = -2 rad/s^2
rc0[1] = 0.2 m
vco[1] = 2 m/s
aco[1] = 3 m/s^2
acor = 2 * cross(om, vco)
vc = cross(om, rc0) + vco
ac = cross(omdot, rc0) + cross(om, cross(om, rc0)) + 2 * cross(om, vco) + aco

# Example 16.20
MKS(deg)
omab = 3 rad/s
alp_ab[3] = 4 rad/s^2
rcd[1] = 0.4 m
rca = [0.4, 0.4 ] m
BEGIN
   om[3] = 1 rad/s
   omdot[3] = 1 rad/s^2
   vcd[1] = 1 m/s
   acd[1] = 1 m/s^2
   vc1 = cross(om, rcd) + vcd
   ac1 = cross(omdot, rcd) + cross(om, cross(om, rcd)) + 2 * cross(om, vcd) + acd
   om_ab[3] = 1 rad/s
   vc2 = cross(om_ab, rca)
   ac2 = cross(alp_ab, rca) - omab^2 * rca
   e1 = vc1 - vc2
   e2 = ac1 - ac2
END
solve(e1[1], e1[2], e2[1], e2[2], om_ab[3], vcd[1], acd[1],  omdot[3])
   
# Example 16.21
MKS(deg, kph, rad/hr, km/hr, km/hr^2)
vb[2] = 600 kph
r = 400 km
abn = (vb[2])^2 / r
abt = -100 km/hr^2
ab = [abn, abt]
om = vb[2] / r; rad/hr
omdot = -abt / r; rad/hr^2
rab[1] = -1 km
aa0[2] = 50 km/hr^2
va[2] = 700 km/hr
om0[3] = om
vab = va - vb - cross(om0, rab)
omdot0[3] = omdot
aab = aa0 - ( ab + cross(omdot0, rab) + cross(om0, cross(om0, rab)) + 2 * cross(om0 , vab))

# Homework Problems:

TBD