E observed. The proposed for a suspended launcher ponents of frequency f 1 and two pendulum model is frequency on the reduce component, using a launchafter the ignition because the CG moved upward owing to seems to become of f 1 , improved object. The dynamics following the rocket has left the launcher the absence littlerocket, decreasing the length of your pendulum. Having said that, the frequency thethe other the significance since it will not impact the launch trajectory. On the other hand, of detailed component, two , decreased. discussion is fnecessary to validate the model and to show the reader how you can recognize the model parameters. 4.1. Double Pendulum Model To acquire a dynamical model from the suspended launcher, we focused around the nonsinusoidal oscillation in the elevation angle, which was observed immediately after ignition. Since these behaviors have been related in each launches in 5-Methyltetrahydrofolic acid site Figure four, only the first launch is consid-Azimuth, deg.The rocket left the rail.Azimuth, deg.Aerospace 2021, eight,ered inside the following discussions. Figure five shows the outcomes in the quick Fourier transformation (FFT) of your elevation angle for the two 14-second time series ahead of ignition (X-15.three s X-1.three s) and just after ignition (X+0.5 s X+14.five s). In each instances, two components of frequency and had been observed. The frequency on the reduce component, , improved just after the ignition because the CG moved upward owing towards the absence of8the of 17 rocket, lowering the length in the pendulum. Even so, the frequency in the other element, , decreased.4.Amplitude, deg.three.five three.0 2.five two.0 1.5 1.0 0.five 0.0 0.0 0.five 1.0 1., Hz Just before Soon after 0.39 0., Hz 0.82 0.Prior to ignition Following ignition two.0 two.5 three.Frequency, HzFigure Spectrum of elevation angle before and immediately after ignition. Figure 5.five. Spectrum of elevation angle ahead of and soon after ignition.To present quantitative explanation of this behavior, the suspended launcher is always to present aaquantitative explanation of this behavior, the suspended launcher is representedas a double pendulum model, asas shown Figure 6. A rigid rod was suspended represented as a double pendulum model, shown in in Figure six. A rigid rod was sususing weightless wire using a with a rigid help. The mass, moment of inertia of the pendedausing a weightless wirerigid support. The mass, CG, andCG, and moment of inrod of the rod were these on the those of the launcher wire connecting the connecting ertia were precisely the same as the similar aslauncher assembly. The assembly. The wirelauncher and hook has length l1 . The hook moves slightly in the horizontal inside the horizontal path; the launcher and hook has length . The hook moves slightly direction; nonetheless, the hook is assumed to be a is assumed to become a rigid help as a result of its drastically larger even so, the hook rigid assistance due to its significantly larger mass (60 kg) in comparison to the launcher assembly. This was additional confirmed was additional confirmed was just about mass (60 kg) in comparison with the launcher assembly. Thisby the fact that the hookby the truth stationary for a number of seconds just after for quite a few seconds immediately after ignition (see that the hook was almost stationary ignition (see Supplemental Video S2). Supplemental MovieThe eigenfrequencies of this model are obtained by solving Euler agrange equations S2). for the attitude angles. of this model are obtained by solving Euler agrange equaThe eigenfrequencies L d L tions for the attitude angles. = 0 (i = 1, two) (four) . – dt i i (four) The Lagrangian is defined as L = – – V. The ( = 1, 2) power comprises two term.