- #1
atat1tata
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I have to deal with the problem of finding an expression for the kinetic energy of a rigid body. One of its point is pivoted to a point that moves arbitrarily. So in order to find an expression for the kinetic energy I use König's theorem, but I need the velocity of the center of mass. I use Euler angles to describe the motion of the fixed frame of reference attached to the principal axes of the body, with the origin of the system in the center of mass of the body.
I know how to find an expression for [itex]\vec\omega[/itex] in the fixed frame of reference, but what I lack is an expression for the velocity of the center of mass (let's say it's a distance [itex]l[/itex] from the pivot) in terms of the velocity of the pivot, the Euler angles and their derivativesThis should be a common problem but I have seen no reference to it in the Internet. So I would be thankful if someone suggests me a book/website/reference to these kinds of problems
I know how to find an expression for [itex]\vec\omega[/itex] in the fixed frame of reference, but what I lack is an expression for the velocity of the center of mass (let's say it's a distance [itex]l[/itex] from the pivot) in terms of the velocity of the pivot, the Euler angles and their derivativesThis should be a common problem but I have seen no reference to it in the Internet. So I would be thankful if someone suggests me a book/website/reference to these kinds of problems