(a) Using the theorem concerning Poisson brackets of vector functions and components of th...

(a) Using the theorem concerning Poisson brackets of vector functions and components of the angular momentum, show that if F and G are two vector functions of the coordinates and momenta only, then

 

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(b) Let L be the total angular momentum of a rigid body with one point fixed and let Lμ, be its component along a set of Cartesian axes fixed in the rigid body. By means of part (a) find a general expression for

 

(Hint: Choose for F and G unit vectors along the μ and v axes.)

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(c) From the Poisson bracket equations of motion for Lμ derive Euler’s equations of motion for a rigid body.