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alrite im new on this forum....just discovered it...pretty awesome
ok, im looking over notes from a classical physics course i did, and ive just covered rigid bodies, and literally just got through the inertia tensor, principal axes and all that good stuff.
theres a step in the gyroscope precession, that is mathematically very simple, but im just having a brain fart and it completely eludes me:
body is roating about a principle axis such that w (rotation vector) is equal to we(3) where e(3) is the principle axes of the body vector (presumably the vector that is perpendicular to the face of the spinning disk)
this means ang mom J=I(3)we(3) where I(3) is the corresponding moment of inertia.
thus the differential of this quantity to get the torque is therefore = 0 as w is constant.
i understand this.....but then
small force F is applied somewhere along this axis at r, this force is perpendicular to w. the body then aquires small component of angular v perpendicular to its axis, new equation of motion, the torque ;J(dot) = r x F.
i also understand this bit, but then this next simple step completely throws me;
if the force is small, the new angular velocity component will be small compared to the angular velocity of the orignal rotation,we can then ignore angular momentum components normal to the axis and therefore write
J(dot) = I(3)w(dot) = r x F
i just do not understand this bit.
if the notation comfuses ive attached the source notes from where im revising. the section is on pages 1718, the notes are good, but i have to say the inertai tensor bit was somewhat lacking in explanation for my taste.
i realise forum etiquette requires i look at old posts and all that, but this quite specific question about a step in a derviation that i simply do not get.
any help appreciated.
cheers
ok, im looking over notes from a classical physics course i did, and ive just covered rigid bodies, and literally just got through the inertia tensor, principal axes and all that good stuff.
theres a step in the gyroscope precession, that is mathematically very simple, but im just having a brain fart and it completely eludes me:
body is roating about a principle axis such that w (rotation vector) is equal to we(3) where e(3) is the principle axes of the body vector (presumably the vector that is perpendicular to the face of the spinning disk)
this means ang mom J=I(3)we(3) where I(3) is the corresponding moment of inertia.
thus the differential of this quantity to get the torque is therefore = 0 as w is constant.
i understand this.....but then
small force F is applied somewhere along this axis at r, this force is perpendicular to w. the body then aquires small component of angular v perpendicular to its axis, new equation of motion, the torque ;J(dot) = r x F.
i also understand this bit, but then this next simple step completely throws me;
if the force is small, the new angular velocity component will be small compared to the angular velocity of the orignal rotation,we can then ignore angular momentum components normal to the axis and therefore write
J(dot) = I(3)w(dot) = r x F
i just do not understand this bit.
if the notation comfuses ive attached the source notes from where im revising. the section is on pages 1718, the notes are good, but i have to say the inertai tensor bit was somewhat lacking in explanation for my taste.
i realise forum etiquette requires i look at old posts and all that, but this quite specific question about a step in a derviation that i simply do not get.
any help appreciated.
cheers
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