Development of a method for computer simulation of a swinging spring load movement path

Synthesis and classification of periodic motion trajectories of the swinging spring load

“…Examples of implementation of this method are given in [33]. A method for finding values of a set of parameters to provide a non-chaotic periodic path of a point load of a swinging spring is given in [34]. Computer animations of corresponding swinging spring oscillations which illustrate the results obtained are shown in [35].…”

“…In the process of constructing periodic paths, we shall rely on studies [31][32][33][34][35]. Therefore, intermediate results will be omitted as far as possible and only final results will be shown.…”

“…Applying algorithms and programs described in [31][32][33][34], solve the system of equations (4) with the values of parameters and initial conditions v(0) = 0; dv(0) = 0.5; u(0) = 1; du(0) = 0. As a result of solution of the system of equations (4), integral curves and phase paths are obtained.…”

“…Determine periodic path for the variable mass m by fixing value of the spring stiffness. Using the procedure given in [31][32][33][34], build the graph of change of the number of pixels in the image of the phase paths depending on mass m, for example, for the value of k = 18.12 ( Fig. 3 and Fig.…”

“…Applying algorithms and programs described in [31][32][33][34], solve the system of equations (7) by numerical Runge-Kutta method with initial conditions v(0) = 0; dv(0) = 1.5; u(0) = 2; du(0) = 0. To determine magnitude of critical value of M, the graph of saturation of the image of the phase path lines [34] can be used. Provide periodicity of the path of the swinging spring load for parameters R = 8, m = 15, k = 150 and h = 2.5 using the found value of M. Fig.…”