 Quartic equation for one component of torque-free angular velocity

ID: quartic-equation-for-one-component-of-torque-free-angular-velocity

Eliminating

ω_{1}^{2}

and

ω_{2}^{2}

between the conserved energy and squared angular momentum gives

\overset{ω}{˙}_{3}^{2} = - \frac{[ L ^{2} - 2 E I _{2} + I _{3} ( I _{2} - I _{3} ) ω _{3}^{2} ] [ L ^{2} - 2 E I _{1} + I _{3} ( I _{1} - I _{3} ) ω _{3}^{2} ]}{I _{1} I _{2} I _{3}^{2}} .

The right-hand side is a quartic polynomial in

ω_{3}

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