Mathematical modeling of the system of drilling rig

Abstract

A nonlinear mathematical model of the system of drilling rig, consisting of the rig, the control cabin, the working platform and platforms with engines has been developed. The mathematical model of the rig with six degrees of freedom is represented by a system of nonlinear ordinary differential equations. The methodology for calculation the basic characteristics of oscillation using the method of polynomial transformations was developed. The formulas for the calculation by the method of polynomial transformations were obtained.

Design and Analysis Based on US Telephone Service Selection Model

“…Assuming only one country has only 3 families, the energy consumption in this country is shown in Figure 3 [9][10].…”

Mathematical modeling of the guidance system of satellite antenna

“…The solution of nonlinear differential equations [18][19][20][21][22][23][24][25] can be carried out various approximate analytical methods [26][27][28][29][30][31][32][33][34][35]: the method of Van der Pol, the harmonic balance method, the averaging method, the small parameter method, the method of Krylov-Bogolyubov, method of harmonic linearization, the method of Poincare. We obtained an approximate analytical solution of the modified method of harmonic linearization with Chebyshev polynomials [36][37][38][39][40][41][42] 2 2 4 2 4 2 2 2 2 3 3 3 3 11 11 11 22 3 15 3 1 2 3 3 3 3 3 Figure 15 shows graphs of the vertical oscillations of mobile satellite antenna obtained by analytical method (blue), a numerical method (yellow) and the graph the oscillation without vibration protection devices (green).…”

On the equation of fourth order with quadratic nonlinearity

“…For the construction of solutions of nonlinear differential equations in partial derivatives [6][7][8][9][10][11][12] is used different analytical and numerical methods: the perturbation methods, the small parameter method, the separation of variables method, the linearization method, the averaging method, the method of the stretched coordinates, the method of composite expansions, grid methods -the method of finite differences and the finite element method [13][14][15][16][17][18][19].…”