from sympy import symbols
from sympy.physics.mechanics import *

dir()

help(ReferenceFrame)

N = ReferenceFrame('N')

dir(N)

v = 1 * N.x + 2 * N.y + 3 * N.z

print(v)

2 * v

v / 3.0

v + v

w = 5 * N.x + 7 * N.y

v - w

dir(v)

v.magnitude()

v.normalize()

v.args

dot(v, w)

cross(v, w)

a1, a2, a3 = symbols('a1 a2 a3')
b1, b2, b3 = symbols('b1 b2 b3')

x = a1 * N.x + a2 * N.y + a3 * N.z
y = b1 * N.x + b2 * N.y + b3 * N.z

dot(x, y)

z = cross(x, y)
z

dot(v, x)

z.diff(a1, N)

A = ReferenceFrame('A')
alpha = symbols('alpha')
A.orient(N, 'Axis', [alpha, N.x])

A.dcm(N)

v.express(A)

z.express(A)

beta, d = dynamicsymbols('beta d')
beta, d

B = A.orientnew('B', 'Axis', (beta, A.y))

vec = d * B.z

B.ang_vel_in(N)

vecdot = vec.dt(N)
vecdot

vecdot.express(N)

theta = dynamicsymbols('theta')
thetad = dynamicsymbols('theta', 1)
theta, thetad