Hi I'm using lagrange mechanics to try and come up with the equation of motion for the system in the image attached.(adsbygoogle = window.adsbygoogle || []).push({});

Two pistons attached to a fly wheel, and are set 90 degrees apart on the wheel. 1 piston is pushed with a force F(t).

The flywheel has inertia I.

After using the lagrange equation I have the three left hand sides of my equaitons of motion.

[tex]M_{1}\ddot{x_{1}}+C_{1}\dot{x}[/tex]=

[tex]Ir^{2}\ddot{\Theta}+0r\dot{\Theta}[/tex]=

[tex]M_{2}\ddot{x_{2}}+C_{2}\dot{x}[/tex]=

But I am struggling to work out the forces for the right hand sides. The is the force pushing piston 1, the flywheel has a moment of inertia, (and a momentum?) and the second piston is well I'm not sure what force this one is equal to... please can someone give me some help here

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# Equation of motion mechanics

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