# Example 20.1
oms[2] = 3 rad/s
omp[3] = -1 rad/s
om = oms + omp
omsdot = cross(omp, oms)
ompdot = 0 * omsdot
omdot = omsdot + ompdot
ra = [0, 1, 0.25] m
va = cross(om, ra)
aa = cross(omdot, ra) + cross(om, cross(om, ra))

# Example 20.2
q = 60 deg
oms = 10 rad/s
omsdot = 6 rad/s^2
omn = 3 rad/s
omndot = 2 rad/s^2
omp = 5 rad/s
ompdot = 4 rad/s^2
om = [-omn, oms * sin(q), omp + oms * cos(q)]
us = [0, sin(q), cos(q)];
ys = omsdot * us  + cross([-omn, 0, omp], oms * us)
yn = [-omndot, 0, 0] + cross([0, 0, omp], [-omn, 0, 0])
yp = [0, 0, ompdot]
alp = ys + yn + yp

# Example 20.3
begin
v = 1 m/s
omx = 1 rad/s
omy = 1 rad/s
omz = 1 rad/s
vd[3] = -v
om = [omx, omy, omz]
rdc = [1, 2, -0.5 ] m
vc[2] = 3 m/s
kin = vc + cross(om, rdc) - vd
y = dot(om, rdc)
end
solve(kin[1], kin[2], kin[3], y, v, omx, omy, omz)

# Example 20.4
OM[3] = 5 rad/s
OMDOT[3] = 2 rad/s^2
ra[1] = 2 m
omp = OM
ompdot = OMDOT
va = cross(omp, ra)
radot = va
aa =  cross(ompdot, ra) + cross(omp, radot)
omM[1] = 3 rad/s
omMdot[1] = 1 rad/s^2
rca[3] = -0.25 m
rcadot[3] = -3 m/s
rcadotdot[3] = -2 m/s^2
vca = rcadot + cross(omM, rca)
aca = rcadotdot + cross(omM, rcadot) + cross(omMdot, rca) + cross(omM, vca)
vc = va + cross(OM, rca) + vca
ac = aa + cross(OMDOT, rca) + cross(OM, cross(OM, rca)) + 2 * cross(OM, vca) + aca

# Example 20.5
OM[1] = 4 rad/s
om1 = OM
OMdot[1] = 1.5 rad/s^2
om1dot = OMdot
rb[3] = -0.5 m
vb = cross(om1, rb)
ab = cross(om1dot, rb) + cross(om1, vb)
om2[3] = 5 rad/s
om2dot[3] = -6 rad/s^2
rcb[2] = 0.2 m
rcbdot[2] = 3 m/s
rcbdotdot[2] = 2 m/s^2
vcb = rcbdot + cross(om2, rcb)
acb = rcbdotdot + cross(om2, rcbdot) + cross(om2dot, rcb) + cross(om2, rcbdot)
vc = vb + cross(OM, rcb) + vcb
ac = ab + cross(OMdot, rcb) + cross(OM, cross(OM, rcb)) + 2 * cross(OM, vcb) + acb

# Homework Problems:

TBD