[SOLVED] Nonlinear-control Homework4 -Accessibility of the N-trailer system

In some special coordinates, the kinematic model of the N-trailer system is described by

We computed dimH2 = n−2 so that H2 = span{ω₁,ω₂,··· ,ω_n−₂}. The two first basis vectors were computed as well as

ω₁ = −x₃dx₁ + dx₂

and

ω₂ = −x₄dx₁ + dx₃

1. Compute the ]              [              H···2 in the form of row vectors∗    ]

0           0    .      Write the corre-

sponding 1-forms ω3 and ωn−2.

2. Check whether ˙ω₁ ∈ H2
3. Check whether ˙ω₂ ∈ H2
4. Check whether ˙ωn−2 ∈ H2
5. Write a basis for H3