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

For a controls class, I am to develop a simulation using AdamsView of a pendulum attached to a link arm and driven by a motor.

The pendulum must start from rest and eventually be balanced at the top of the link arm.

I am stuck at deriving the equations of motion right now. We are to use Langrangian for developing the equations.

2. Relevant equations

These are the energy equations for the system

The kinetic energy of the entire device is:

K=1/2I_{d}O'[t]^{2}+1/4(2(2I_{l}+L^{2}m)B'[t]^{2}+4Lmr cos[B[t]]B'[t]O'[t]+(2I_{l}+L^{2}m+2mr^{2}-(2I_{l}+L^{2}m)cos[2[B[t]])O'[t]^{2})

The potential energy is:

P=gLm cos[B[t]]

The work of the motor is:

W=TO[t]

Paramaters(meters, kilograms, seconds)

Centroidal moment of inertia of the inverted link I_{l}=0.0000343

Centroidal moment of inertia of the driver link I_{d}=0.000687

Distance from the driver axis to the hinge of the inverted link, r=0.1079

Distance from the end to the centroid of the inverted link, L=0.16

Mass of the driving bar (the horizontal one), m=0.127

Mass of the inverted link, m_{d}=0.0249

O=theta

B=beta

I've attached a diagram of this.

3. The attempt at a solution

Now will deriving with respect to thetas give the equation of motion for the driving link and then with respect to my betas I will get the equation for the inverted link?

I am also not sure what part the work of the motor plays in this. After deriving the equations, will they both be set equal to the work of the motor?

Any help would be greatly appreciated. Thanks

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# Equation of Motion: Inverted Pendulum

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