(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Derive all equations necessary to model θ.

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

τ_{net}= τ + Lmg sin(θ) /2 . . . (1)

From net torque to the angular acceleration:

α = τ_{net}/I . . . (2)

Integrals and derivatives:

θ = θ_{o}+ ω_{o}t + 0.5α_{o}t^{2}. . . (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 = τ_{net}/I = τ_{net}= (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?

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# Homework Help: Segway physics question

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