PeteSampras
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"A rigid lamina (i.e. a two dimensional object) has principal moments of inertia about the centre of mass given by ##I_1=u^2-1##, ##I_2=u^2+1##, ##I_3=2u^2##
Choose the initial angular velocity to be ##ω = µN \hat{e_1} + N \hat{e_2}##. Define tan α = ω2/ω1,
which is the angle the component of ω in the plane of the lamina makes with e1. Show that it satisfies:
##\ddot{α}+ N^2 \cos α \sin α = 0##"
(the problem does not says what is N). The problem is on http://www.damtp.cam.ac.uk/user/tong/dynamics/mf3.pdf
I tried used the Euler equation, considering that ##N_1=N_2=0##
My Euler equation are:
##\dot{\omega_1}+ \omega_2 \omega_3=0##
##\dot{\omega_2}- \omega_1 \omega_3=0##
##2 \mu^2 \dot{\omega_3}+2 \omega_1 \omega_3 =N_3##
I tried of several ways of combining this equations , using that tan α = ω2/ω1, but i do not get to ##\ddot{α} + N^2 \cos α \sin α = 0##.
¿some hint please?
Some Hint to do this exercice this?...
Choose the initial angular velocity to be ##ω = µN \hat{e_1} + N \hat{e_2}##. Define tan α = ω2/ω1,
which is the angle the component of ω in the plane of the lamina makes with e1. Show that it satisfies:
##\ddot{α}+ N^2 \cos α \sin α = 0##"
(the problem does not says what is N). The problem is on http://www.damtp.cam.ac.uk/user/tong/dynamics/mf3.pdf
I tried used the Euler equation, considering that ##N_1=N_2=0##
My Euler equation are:
##\dot{\omega_1}+ \omega_2 \omega_3=0##
##\dot{\omega_2}- \omega_1 \omega_3=0##
##2 \mu^2 \dot{\omega_3}+2 \omega_1 \omega_3 =N_3##
I tried of several ways of combining this equations , using that tan α = ω2/ω1, but i do not get to ##\ddot{α} + N^2 \cos α \sin α = 0##.
¿some hint please?
Some Hint to do this exercice this?...