Hi there,(adsbygoogle = window.adsbygoogle || []).push({});

the Focault compass its supposed to be a fast spinning disk that keeps pointing to the earth north

the spinning axis is mounted on top of a rotating base, angle which is supposed to oscillate when slighty displaced from the north direction

is this oscilatory behaviour occuring 'only' on the earth surface, or its true also in inertial far-away-from-earth frames?

i wrote the lagrangian for this thing using omega . I omega

lets assume first the problem in far-awar-from-earth-inertial frames, then i got a fixed basisEx,EyandEz

the gyroscope has its principal axis likeEz,EnandEw, whereEn= cos(a)Ex+ sin(a)Ey

andEw= -sin(a)Ex+ cos(a)Ey

the spinning axis of the gyroscope isEn, which is also the symmetry axis

the gyroscope can also rotate in theEzaxis, with an angle a

so i wrote the I tensor in dyadic rep. likeI= IzEzEz+ IrEnEn

butEnEn= cos(a)^2ExEx+ sin(a)cos(a) [ExEy+EyEx] + sin(a)^2EyEy

the rotation of the gyroscope can be represented as:

omega= a'Ez+ omegaEn= a'Ez+ omega cos(a)Ex+ omega sin(a)Ey

so when you plug this rotation into the inertia tensor to get the kinetic energy, you get at the end:

Lagrangian = a'^2 Iz + omega^2 Ir

(remember that the dyads act with vectors likeEiEj*Ek= (Ej . Ek)Ei, where.is the dot product between vectors)

so as you see, my lagrangian does NOT depend on a, so i cant get an oscillatory motion in this system

Im doing something blatantly wrong here?

any insights are welcome

Cheers

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Focault's compass

**Physics Forums | Science Articles, Homework Help, Discussion**