Why coning motion occurs ?

1. May 2, 2013

skoo

axisymmetric bodies tend to rotate on its own axis while moving which is know as coning. why does it occur ? what are the forces which making it rotate ? what is the reason for this turning moment(coning) ??

2. May 2, 2013

Danger

Your question confuses me greatly. Unless we have a bit of a language barrier, there is no inherent reason that an axisymmetric object will rotate. That's why we have rifling cut into gun barrels and the fletching on arrows attached at an angle and why a quarterback has to twist his wrist when throwing a pigskin. Gyroscopic stability must be imparted from without.

3. May 3, 2013

jhae2.718

Consider Euler's equations for a rigid body with a body-fixed reference frame aligned with the principal axes of inertia:
\begin{align*} I_1\dot{\omega}_1 + \underline{(I_3 - I_2)\omega_2\omega_3} &= L_1 \\ I_2\dot{\omega}_2 + \underline{(I_1 - I_3)\omega_3\omega_1} &= L_2 \\ I_3\dot{\omega}_3 + \underline{(I_2 - I_1)\omega_1\omega_2} &= L_3 \end{align*}
(More generally, $\dot{\boldsymbol{h}}_\mathrm{c} = \boldsymbol{L}_\mathrm{c}$)
Note the underlined coupling terms. These cause rotation/moments about one axis to affect the other two. This is why rotation results in precession and nutation.

Last edited: May 3, 2013
4. May 3, 2013

5. May 3, 2013

Danger

Obviously, I am the one who had a language barrier with the question. I was thinking only of stand-alone objects (particularly projectiles) when I posted my rather premature response. Sorry.

6. May 3, 2013

skoo

thank you.. the riddle is half solved for me.. can you give me some more information regarding the external forces in hydrodynamics point of view, that are acting on axisymmetric body which causes rotation about its axis? apart from munk moment.

thank you..