I've been working on this problem for a while and here comes the problem: I'm building a balancing system for a bicycle using Gyroscopic effect (take a look at Figure 2 for more details). My system consists of 2 parts:(adsbygoogle = window.adsbygoogle || []).push({});

All parameters are given. The question is I have to derive formula for calculating

- the bicycle itself
- a flywheel on top of it
total kinetic energy of the system. Figure 1 is the formula given in the article but I'm a bit confused about how to get it. I can understand the first 3 terms in the formula like this:

(1) translational kinetic energy of the bike's center of mass

(2) translational kinetic energy of the flywheel's center of mass

(3) rotational kinetic energy of the bike about its center of mass

Fig. 1

Since the last 3 terms in the given expression involve moment of inertia, I guess these are rotational kinetic energy of the flywheel about some reference which I don't know yet.

Please tell me how to get these last 3 terms. I would be very appreciated for your help.

Fig. 2

Reference: see attached PDF file

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# Problem finding the total kinetic energy of bicycle system

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