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Mystery of the top

From the very complicated equations of motions follows that the quantity

G = r L_z - a L₃

with

L_z:

partion of the angular momentum in z direction

L₃:

partion of the angular momentum in direction of the figure axis (=symmetry axis)

changes its magnitude very slowly. So we call it an "quasi-conservation quantity". (If there is no contact area, the above quantity would be exactly constant!) Note that as a consequence of the transition on the stem, there is an "parameter change" (i.e. a becomes a', r becomes r' and G changes to G'). One can show however, that G' and G are almost equal.

The amazing existence of an conservation quantity (when we speak from an "integral of the motion" or "the conservation quantity" we always mean our "quasi-conservation quantity") leads us ...

to the next section: Explanation of the sit up