Lagrange constraint mechanics problem

DylanG

Just a simple question. I can see that for this to work I need:

T_rot = 1/5 ma²(thetaDOT + phiDOT)²

Just can't work out what phi has to do with rotational kinetic energy. I would have thought it would need to be simply the same thing but without the phiDOT term.

diazona

[itex]\theta[/itex] is the angular position of an identified point on the smaller sphere, measured with respect to the line joining the centers of the two spheres, right? Note that not only does [itex]\theta[/itex] change with time, but so does the orientation of that joining line, so you need to take that into account as well. That's where the [tex]\dot\phi[/tex] comes from.

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DylanG	Lagrange constraint mechanics problem Tweet Just a simple question. I can see that for this to work I need: T_rot = 1/5 ma²(thetaDOT + phiDOT)² Just can't work out what phi has to do with rotational kinetic energy. I would have thought it would need to be simply the same thing but without the phiDOT term.

diazona Recognitions: Homework Help	[itex]\theta[/itex] is the angular position of an identified point on the smaller sphere, measured with respect to the line joining the centers of the two spheres, right? Note that not only does [itex]\theta[/itex] change with time, but so does the orientation of that joining line, so you need to take that into account as well. That's where the [tex]\dot\phi[/tex] comes from.