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Segway physics question

  1. Dec 8, 2008 #1
    1. The problem statement, all variables and given/known data
    Derive all equations necessary to model θ.
    [​IMG]
    In the figure, ω is the angular velocity of the body about the axle. v is the linear velocity of the axle. The body supplies a clockwise torque τ to the axle.

    2. Relevant equations


    3. The attempt at a solution

    The net torque acting on the body at A

    τnet = τ + Lmg sin(θ) /2 . . . (1)

    From net torque to the angular acceleration:

    α = τnet/I . . . (2)

    Integrals and derivatives:

    θ = θo + ωot + 0.5αot2 . . . (3)

    ω = dθ/dt . . . (4)

    α = dω/dt . . . (5)


    Linearize: If the device is initially vertical and at rest, and θ is always small:

    dθ/dt = ω . . . (6)

    dω/dt = α = τnet/I = τnet = (Lmg/2I) θ + (1/I) τ . . . (7)

    Let x := [ θ ; ω ], u = τ :

    x' = Ax + Bu = [ 0 1 ; Lmg/2I 0 ] x + (1/I) τ . . . (8)

    y = Cx + Du = [ 1 0 ] x . . . (9)

    Is this all I need to consider for θ?

    - Thanks
     
  2. jcsd
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