Kapitza Pendulum: A Physically Transparent Simple Explanation
نویسنده
چکیده
The phenomenon of dynamic stabilization of the inverted pendulum whose pivot is forced to oscillate with a high frequency in vertical direction is revisited. A simple physically meaningful explanation of the phenomenon is presented, followed by the derivation of an approximate quantitative criterion of stability. A computer program simulating the physical system is developed, which aids the analytical investigation of the phenomenon in a manner that is mutually reinforcing. Material is appropriate for undergraduate university students.
منابع مشابه
Kapitza’s Pendulum: A Physically Transparent Simple Treatment
The phenomenon of dynamic stabilization of the inverted rigid planar pendulum whose pivot is forced to oscillate at a high frequency in the vertical direction is revisited. This intriguing nonlinear physical system is analyzed in the paper using time-scale separation and averaging. On this basis, a simple and clear physically meaningful explanation of the phenomenon is presented, followed by th...
متن کاملDynamic Stabilization of the Inverted Pendulum
The inverted pendulum is a canonical problem in both Nonlinear Dynamics and Control Theory. In this article, the phenomenon of dynamic stabilization of the vertically driven inverted pendulum is investigated experimentally and numerically. We resolve the first stabilizing boundary in driving parameter space, as well as investigate the effects of frictional damping on the dynamics of the pendulu...
متن کاملInverted-pendulum Model for the Stability of Bouncing Droplets on Vibrating Foundation
We investigate experimentally liquid (oil) droplets vibrating over a bath of the same liquid and relate the phenomenon to the well-known effect of the stabilization of an inverted pendulum on a vibrating foundation (a “Kapitza pendulum”). Small fast vibrations can be substituted by an effective “levitation” force. We further discuss this effective stabilizing “spring force”. Besides the inverte...
متن کاملNonlinear phase dynamics in a driven bosonic Josephson junction.
We study the collective dynamics of a driven two-mode Bose-Hubbard model in the Josephson interaction regime. The classical phase space is mixed, with chaotic and regular components, which determine the dynamical nature of the fringe visibility. For a weak off-resonant drive, where the chaotic component is small, the many-body dynamics corresponds to that of a Kapitza pendulum, with the relativ...
متن کاملNumerical solution of higher index DAEs using their IAE's structure: Trajectory-prescribed path control problem and simple pendulum
In this paper, we solve higher index differential algebraic equations (DAEs) by transforming them into integral algebraic equations (IAEs). We apply collocation methods on continuous piece-wise polynomials space to solve the obtained higher index IAEs. The efficiency of the given method is improved by using a recursive formula for computing the integral part. Finally, we apply the obtained algo...
متن کامل