What Causes Coning in Axisymmetric Bodies?

[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) ??

 

[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.

 

[jhae2.718]

Consider Euler's equations for a rigid body with a body-fixed reference frame aligned with the principal axes of inertia:
<br /> \begin{align*}<br /> I_1\dot{\omega}_1 + \underline{(I_3 - I_2)\omega_2\omega_3} &amp;= L_1 \\<br /> I_2\dot{\omega}_2 + \underline{(I_1 - I_3)\omega_3\omega_1} &amp;= L_2 \\<br /> I_3\dot{\omega}_3 + \underline{(I_2 - I_1)\omega_1\omega_2} &amp;= L_3<br /> \end{align*}<br />
(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.

 

[OCR]

what are the forces which making it rotate?

http://en.wikipedia.org/wiki/Hunting_oscillation

http://en.wikipedia.org/wiki/Adhesion_railway#Directional_stability_and_hunting_instability

http://en.wikipedia.org/wiki/Pilot-induced_oscillation





OCR

 

[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.

 

[skoo]

Consider Euler's equations for a rigid body with a body-fixed reference frame aligned with the principal axes of inertia:
<br /> \begin{align*}<br /> I_1\dot{\omega}_1 + \underline{(I_3 - I_2)\omega_2\omega_3} &amp;= L_1 \\<br /> I_2\dot{\omega}_2 + \underline{(I_1 - I_3)\omega_3\omega_1} &amp;= L_2 \\<br /> I_3\dot{\omega}_3 + \underline{(I_2 - I_1)\omega_1\omega_2} &amp;= L_3<br /> \end{align*}<br />
(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.

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..