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stroustroup

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Wikipedia claims that the Chandler wobble (a deviation of the angular velocity vector of the Earth with respect to the principal axis) is a nutation (see http://en.wikipedia.org/wiki/Chandler_wobble).

But suppose we choose our inertial frame so that the Earth's angular momentum points in the +z direction. Then (ignoring gravitational forces from other bodies) the angles of the principal axis and the angular velocity with respect to the z axis are both constant (nutation angle is constant when there are no torques). Moreover, the angular velocity vector, principal axis and angular momentum all lie on the same plane. The principal axis and angular velocity precess around the z axis at a frequency of 2π/day, while the Earth is aditionally spinning (as in change of the third euler angle) about the principal axis at a period of 1/300 days. In the body frame, this corresponds to the precession of the angular velocity vector about the North pole.

If I understand correctly, this is what we call the "Chandler wobble", and it has a period of 435 days (not 300 because the Earth is not a rigid body). But this movement is not a nutation, but rather a precession.

So, what is the nutation in the Chandler wobble? I've also read stuff where "nutation" and "free precession" appear to be synonymous. This is very confusing.

EDIT: Also see http://farside.ph.utexas.edu/teaching/celestial/Celestial/node72.html This also says that the wobble is a precession, but instead it is the precession of the principal axis around the angular momentum, which has a frequency of almost a day.

But suppose we choose our inertial frame so that the Earth's angular momentum points in the +z direction. Then (ignoring gravitational forces from other bodies) the angles of the principal axis and the angular velocity with respect to the z axis are both constant (nutation angle is constant when there are no torques). Moreover, the angular velocity vector, principal axis and angular momentum all lie on the same plane. The principal axis and angular velocity precess around the z axis at a frequency of 2π/day, while the Earth is aditionally spinning (as in change of the third euler angle) about the principal axis at a period of 1/300 days. In the body frame, this corresponds to the precession of the angular velocity vector about the North pole.

If I understand correctly, this is what we call the "Chandler wobble", and it has a period of 435 days (not 300 because the Earth is not a rigid body). But this movement is not a nutation, but rather a precession.

So, what is the nutation in the Chandler wobble? I've also read stuff where "nutation" and "free precession" appear to be synonymous. This is very confusing.

EDIT: Also see http://farside.ph.utexas.edu/teaching/celestial/Celestial/node72.html This also says that the wobble is a precession, but instead it is the precession of the principal axis around the angular momentum, which has a frequency of almost a day.

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