Abstract
The behavior of a spatial double pendulum (SDP), comprising two pendulums that swing in different planes, was investigated. Movement equations (i.e., mathematical model) were derived for this SDP, and oscillations of the system were computed and compared with experimental results. Matlab computer programs were used for solving the nonlinear differential equations by the Runge-Kutta method. Fourier transformation was used to obtain the frequency spectra for analyses of the oscillations of the two pendulums. Solutions for free oscillations of the pendulums and graphic descriptions of changes in the frequency spectra were used for the dynamic investigation of the pendulums for different initial conditions of motion. The value of the friction constant was estimated experimentally and incorporated into the equations of motion of the pendulums. This step facilitated the comparison between the computed and measured oscillations.
Highlights
Research on different kinds of pendulum, including the double pendulum in a plane (PDP), has spanned more than three centuries, starting with the invention of the pendulum clock in 1657
Two hundred a fifty years later, research on a pendulum with vertical oscillations of the hinge showed the influence of the moving suspension point on the oscillations [15]
These early studies were followed by investigations of other types of pendulum, such as, an inverted pendulum with an oscillating suspension point under various conditions [4, 10]; the PDP [7, 3], including the so-called spherical pendulum [5]; and various pendulums with an oscillating motion of the base hinge [13, 14]
Summary
Research on different kinds of pendulum, including the double pendulum in a plane (PDP), has spanned more than three centuries, starting with the invention of the pendulum clock in 1657. We have shown that a combined numerical-analytical approach enables us to describe some features of the complex motion of the two pendulums under consideration and thereby to obtain estimations of some important system characteristics (number of frequencies and their values). Graphical solutions for free oscillations and graphical descriptions of the change in frequency constituted the basis of the research on the dynamics of the SDP for different parameter values and initial conditions. To find a solution to this question, the following steps were taken: formulating the dynamic model by applying the Lagrange method and finding solutions for small and non-small values of the angles φi (i = 1,2), respectively; obtaining graphical solutions for free oscillations and graphical descriptions of the. Changes in the frequency spectra by using Fourier transformations for different parameter values and initial conditions
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
