To obtain the equations of motion for this device, the z direction is ignored, and then a complex number is introduced to solve the coupled differential equations for x and y. For 10 points each:
[10m] Name this device whose plane of oscillation has an angular velocity equal to the Earth’s angular velocity times the cosine of colatitude.
ANSWER: Foucault (“foo-koh”) pendulum [or Foucault’s pendulum] (It is named after Léon Foucault.)
[10e] The forces on the Foucault pendulum include this fictitious force that deflects objects rightward in the Northern Hemisphere.
ANSWER: Coriolis force
[10h] This operation can be used to explain the rotation of the plane of oscillation. Given del as the covariant derivative induced by a connection between the tangent bundle of a manifold and the manifold, this operation moves a vector field X along a smooth curve while keeping “del X” equal to zero.
ANSWER: parallel transport
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