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- Kapitzas_pendulum abstract "Kapitza's pendulum is a rigid pendulum in which the pivot point vibrates in a vertical direction, up and down. It is named after Russian Nobel laureate physicist Pyotr Kapitza, who in 1951 developed a theory which successfully explains some of its unusual properties. The unique feature of the Kapitza pendulum is that the vibrating suspension can cause it to balance stably in an inverted position, with the bob above the suspension point. In the usual pendulum with a fixed suspension, the only stable equilibrium position is with the bob hanging below the suspension point; the inverted position is a point of unstable equilibrium, and the smallest perturbation moves the pendulum out of equilibrium. In nonlinear control theory the Kapitza pendulum is used as an example of a parametric oscillator that demonstrates the concept of \"dynamic stabilization\".The pendulum was first described by A. Stephenson in 1908, who found that the upper vertical position of the pendulum might be stable when the driving frequency is fast Yet until the 1950s there was no explanation for this highly unusual and counterintuitive phenomenon. Pyotr Kapitza was the first to analyze it in 1951. He carried out a number of experimental studies and as well provided an analytical insight into the reasons of stability by splitting the motion into \"fast\" and \"slow\" variables and by introducing an effective potential. This innovative work created a new subject in physics, that is vibrational mechanics. Kapitza's method is used for description of periodic processes in atomic physics, plasma physics and cybernetical physics. The effective potential which describes the \"slow\" component of motion is described in \"Mechanics\" volume of the Landau's Course of Theoretical Physics.Another interesting feature of the Kapitza pendulum system is that the bottom equilibrium position, with the pendulum hanging down below the pivot, is no longer stable. Any tiny deviation from the vertical increases in amplitude with time. Parametric resonance can also occur in this position, and chaotic regimes can be realized in the system when strange attractors are present in the Poincaré section .".
- Kapitzas_pendulum thumbnail Kapitza_pendulum.svg?width=300.
- Kapitzas_pendulum wikiPageID "31437286".
- Kapitzas_pendulum wikiPageLength "13017".
- Kapitzas_pendulum wikiPageOutDegree "32".
- Kapitzas_pendulum wikiPageRevisionID "684260684".
- Kapitzas_pendulum wikiPageWikiLink Atomic_physics.
- Kapitzas_pendulum wikiPageWikiLink Attractor.
- Kapitzas_pendulum wikiPageWikiLink Category:Pendulums.
- Kapitzas_pendulum wikiPageWikiLink Chaos_theory.
- Kapitzas_pendulum wikiPageWikiLink Closed_system.
- Kapitzas_pendulum wikiPageWikiLink Coupling_constant.
- Kapitzas_pendulum wikiPageWikiLink Course_of_Theoretical_Physics.
- Kapitzas_pendulum wikiPageWikiLink Cybernetical_physics.
- Kapitzas_pendulum wikiPageWikiLink Double_scaling_limit.
- Kapitzas_pendulum wikiPageWikiLink Effective_potential.
- Kapitzas_pendulum wikiPageWikiLink Euler–Lagrange_equation.
- Kapitzas_pendulum wikiPageWikiLink Kinetic_energy.
- Kapitzas_pendulum wikiPageWikiLink Lagrangian_mechanics.
- Kapitzas_pendulum wikiPageWikiLink Lev_Landau.
- Kapitzas_pendulum wikiPageWikiLink Mechanical_equilibrium.
- Kapitzas_pendulum wikiPageWikiLink Nobel_Prize.
- Kapitzas_pendulum wikiPageWikiLink Nonlinear_control.
- Kapitzas_pendulum wikiPageWikiLink Parametric_oscillator.
- Kapitzas_pendulum wikiPageWikiLink Pendulum.
- Kapitzas_pendulum wikiPageWikiLink Pendulum_(mathematics).
- Kapitzas_pendulum wikiPageWikiLink Pendulum_clock.
- Kapitzas_pendulum wikiPageWikiLink Perturbation_theory_(quantum_mechanics).
- Kapitzas_pendulum wikiPageWikiLink Plasma_(physics).
- Kapitzas_pendulum wikiPageWikiLink Poincaré_map.
- Kapitzas_pendulum wikiPageWikiLink Potential_energy.
- Kapitzas_pendulum wikiPageWikiLink Pyotr_Kapitsa.
- Kapitzas_pendulum wikiPageWikiLink Virial_theorem.
- Kapitzas_pendulum wikiPageWikiLink Walking.
- Kapitzas_pendulum wikiPageWikiLink File:KapitzaPendulumScheme.gif.
- Kapitzas_pendulum wikiPageWikiLink File:Kapitza_pendulum.svg.
- Kapitzas_pendulum wikiPageWikiLinkText "Kapitza%27s_pendulum".
- Kapitzas_pendulum wikiPageWikiLinkText "Kapitza's pendulum".
- Kapitzas_pendulum wikiPageUsesTemplate Template:Reflist.
- Kapitzas_pendulum subject Category:Pendulums.
- Kapitzas_pendulum hypernym Pendulum.
- Kapitzas_pendulum type Dynamic.
- Kapitzas_pendulum type Object.
- Kapitzas_pendulum type Redirect.
- Kapitzas_pendulum comment "Kapitza's pendulum is a rigid pendulum in which the pivot point vibrates in a vertical direction, up and down. It is named after Russian Nobel laureate physicist Pyotr Kapitza, who in 1951 developed a theory which successfully explains some of its unusual properties. The unique feature of the Kapitza pendulum is that the vibrating suspension can cause it to balance stably in an inverted position, with the bob above the suspension point.".
- Kapitzas_pendulum label "Kapitza's pendulum".
- Kapitzas_pendulum sameAs Q4286430.
- Kapitzas_pendulum sameAs m.0gkyb58.
- Kapitzas_pendulum sameAs Маятник_Капицы.
- Kapitzas_pendulum sameAs Q4286430.
- Kapitzas_pendulum wasDerivedFrom Kapitzas_pendulum?oldid=684260684.
- Kapitzas_pendulum depiction Kapitza_pendulum.svg.
- Kapitzas_pendulum isPrimaryTopicOf Kapitzas_pendulum.
