Analytical Mechanics by Carl S. Helrich

Author:Carl S. Helrich
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

in which the term is represented in the fixed system (see (4.53)). The point is not fixed in space, but is a point on the turntable and has the velocity of the point on the turntable. Noting that the point

is, simultaneously, a point on the rigid body and a point on the turntable, the velocity of is . That is

since is parallel to the turntable angular velocity . The rolling constraint is then

represented in the fixed system.

The abstract form of the kinetic energy of rotation is

For a sphere the elements of the inertia tensor are . For the sphere then

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