Egg Shaped Egg

From the previous post "Lay Another Egg..." dated 12 Jul 2016,

$|F^{*}_{c}|=|F_{drag}|sin(\theta)=\delta m.r.\omega^2$

where $\delta m$ is an elemental mass on the surface of the egg. $r$ is the radial distance from the axis along the direction of travel and $\theta$ the angle at the $C.G$ between $F_{drag}$ and the rotational axis.

$r=\cfrac{|F_{drag}|}{\delta m.\omega^2}sin(\theta)$

This is not a polar plot, $r$ is the distance from the horizontal rotational axis.

$y_g=r$

The distance along the rotational axis of $\delta m$ from the $C.G$ is given by,

$x_g=rcos(\theta_1)=\cfrac{|F_{drag}|}{\delta m.\omega^2}sin(\theta)cos(\theta_1)$

This may be wrong Pls refer to "Nothing To Do...With An Egg" dated 13 Jul 2016

We plot the parametric pair,

$x=1-sin(\cfrac{\pi}{2}-s)*cos(s)$ and

$y=sin(\cfrac{\pi}{2}-s)$

$0\le s\le\pi/2$

Implemented in the plotting software, $s$ is measured with reference to the $y=0$ axis.  In the intended graph, $\theta$ starts at $s=\pi/2$ at the front tip and ends with $s=0$ at the half circle defined by an axis that divides the particle into front and back.  $\theta_1$ is always measured with reference to the $x=0$ axis and start from $0$ to $\pi$ and varies linearly with $s$. So, $\theta\rightarrow (\pi/2-s)$ and $\theta_1\rightarrow s$.  Up to this point, the  front tip will be at the origin where $s=0$, to invert the plot $x\rightarrow 1-x$.

As spin, $\omega$, increases, the front tip sharpens.  As drag force, $|F_{drag}|$, increases, the front tip flattens.  The ratio,

$R_D=\cfrac{|F_{drag}|}{\omega^2}$

a drag-spin ratio determines the shape of the particle.

The front tip is always flat as $\delta m$ moves tangentially away under the action of $F_c$ a centripetal force.  The front top does not sharpen with a discontinuity in gradient.

What happen to the back of the particle?