Boundary Conditions on Fast Oscillation and Pivot Oscillation Speeds in n-Chain Kapitza Pendulum Systems
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This study investigates the stability conditions for an n-chain Kapitza pendulum system. A single Kapitza pendulum has an interesting property in that its stable equilibrium position is the upright position. The motion of the pendulum can be separated into a small-yet-fast component and a large-yet-slow component. This property extends to the π-chain system. This study, through the separation of scales technique, confirms that the small, fast component does not diverge with π and finds the criteria for the stability of the πth pendulum. In doing so, this study also finds an upper bound for the sum of the fast components. Additionally, numerical simulations of the π-chain Kapitza system showed a trend of increasing unstable states with π.
