Pole cone

When moving a symmetrical top with a support point, the imaginary, body-fixed pole cone is formed from the movement of the momentary axis of rotation around the figure axis . The Polkegel will Gangpolkegel or polhode cone called (from ancient Greek πόλος Polos , "axis", ὁδός Hodos , "way street"). ${\displaystyle {\vec {\omega }}}$

The point angle of the pole cone (between the outer surface of the pole cone and the figure axis) can be derived from Euler's gyroscopic equations as follows: ${\displaystyle \gamma }$

${\displaystyle \gamma =\arctan {\frac {\omega _{\perp }}{\omega _{\|}}}}$

with the two components of the angular velocity perpendicular and parallel to the figure axis. ${\displaystyle \omega }$

The general definition summarizes the Polkegel than the roundabout from the axis of rotation on Avoided area which need not be tapered and on the axis of rotation in the space swept lane bowling gleitungslos rolls, see literature.

See also

• Track cone and pole cone
• Geometric description of the nutation of the symmetrical Euler top
• Curve gyro
• Poinsot construction with polhodia lying on the pole cone.
• Gangpolbahn , which is currently rolling on the Rastpolbahn .

literature

• K. Magnus : Kreisel: Theory and Applications . Springer, 1971, ISBN 978-3-642-52163-8 , pp. 27 f . ( Limited preview in Google Book Search [accessed February 20, 2018]).