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Spherical pendulum small oscillations for slewing crane motion.

Alexander V Perig1, Alexander N Stadnik2, Alexander I Deriglazov2

  • 1Manufacturing Processes and Automation Engineering Department, Engineering Automation Faculty, Donbass State Engineering Academy, Shkadinova 72, Donetsk Region, Kramatorsk 84313, Ukraine.

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Summary
This summary is machine-generated.

This study analyzes spherical pendulum oscillations using Lagrange mechanics, detailing natural frequencies and payload motion for a rotating crane boom. Results accurately match experimental observations.

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Area of Science:

  • Mechanical Engineering
  • Physics
  • Applied Mathematics

Background:

  • Spherical pendulums are fundamental in physics and engineering.
  • Understanding oscillations in rotating systems is crucial for applications like crane dynamics.

Purpose of the Study:

  • To describe small oscillations of a spherical pendulum with a rotating suspension center using Lagrange mechanics.
  • To derive analytical solutions for natural frequencies and payload paths in a rotating crane boom scenario.
  • To analyze amplitude-frequency characteristics and cable tension.

Main Methods:

  • Lagrange mechanics formulation for pendulum dynamics.
  • Analytical derivation of natural frequencies and payload trajectories.
  • Numerical analysis of amplitude-frequency characteristics and cable tension.
  • Comparison of computational results with experimental data.

Main Results:

  • Analytical solutions for natural frequencies and payload paths were obtained in inertial and non-inertial frames.
  • Numerical amplitude-frequency characteristics of relative payload motion were determined.
  • An analytical expression and numerical estimation for cable tension force were proposed.
  • Computational results demonstrated high accuracy in correlation with experimental observations.

Conclusions:

  • The Lagrange mechanics approach provides an effective framework for analyzing rotating spherical pendulum dynamics.
  • The derived solutions and numerical estimations are validated by experimental data, offering practical insights for crane boom operations.