Motion of A Top with Time-Varying Mass Properties
Inspired by Inception
The movie Inception directed by Christopher Nolan is my all-time favorite. The top in the end scene started wiggling a bit gives us the impression that Cobb went back in reality, because friction exists.
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For a dynamics course project at Purdue, I decided to study the motion of a top and simulate it by varying its mass properties. I want to find out, without the effect of friction, whether the top can still wiggle and further prove the possibility that Cobb is still in a dream.
Approach to the result
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Create a 3D model of the top and get the mass properties from Solidworks
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Use the Lagrangian to find the equations of motion
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Assuming there's a fuel tank in the top and its mass properties vary with time
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Solve the EOMs with Matlab and Simulink for both constant mass and varying mass by feeding in multiple initial conditions
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Plot the tip motion in 3D space and compare the trajectory
As we can see from the trajectory, with a constant mass, the top will form will form a closed precessional trajectory. But if the top is consuming fuel when it spins, the top will form an increasing nutation and sping frequency, which might be seen as the "wiggling" motion. So is it a dream or not...
Constant mass
Varying mass
