The initial XXXXXXXXXXEuler angles yaw, pitch and roll of a vehicle are (\psi, \theta, \phi)(ψ,θ,ϕ) = (40, 30, 80) degrees. Assume the body angular velocity vector of the craft is given through the BB...

The initial (3-2-1) Euler angles yaw, pitch and roll of a vehicle are


$(\psi, \theta, \phi)$



(
ψ
,

θ
,

ϕ
)




= (40, 30, 80) degrees. Assume the body angular velocity vector of the craft is given through the


$B$



B




frame components as













B











ω









ω


=



⎡
⎣









sin

(
0.1
t
)






0.01






cos

(
0.1
t
)









⎤
⎦



20
deg/s



. Write a program to numerically integrate the yaw, pitch and roll angles over a simulation time of 1 minute. Enter the Euler angle norm


$\sqrt{\psi^2 + \theta^2 + \phi^2}$











ψ







2








+


θ







2








+


ϕ







2














​











at the simulation time step 42s. Express angles in radians.

[Hint: if you are unsure, look at the "Optional Review: Integrating Differential Kinematic Equations" video.]

[​Hint: In the integration, start with the initial angles and just integrate them without mapping them to specific quadrants. ]