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Unformatted text preview: e equilibrium because coeﬃcient before 4l is
4) Balance of force
In non-inertial rotational reference frame there are three forces acting on the
point mass: gravitational force mg acting downward, centrifugal force m⌦2 l sin ✓0
acting outward from rotational orbit and reaction force of the wire m⌦2 sin ✓0 cos ✓0 l+
mg sin ✓0 pointing perpendicular to it . These three forces balance each other.
It is possible to obtain the expression for the reaction force using the method
of Lagrange multipliers.
L = m l˙2 + m l2 ✓2 + m ⌦2 l2 sin2 ✓0 mgl cos ✓0 ,
f (✓) = ✓ = ✓0 - constraints.
Equation of motion with constraints:
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