Variational approach to the construction of discrete mathematical model of the pendulum motion with vibrating suspension with friction

The main purpose of this work is, first, a construction the indirect Hamilton’s variational principle for problem motion pendulum with vibration suspension friction, oscillating along straight line making small angle vertical line. Second, on its basis difference scheme. Third, to carry out investigation by methods numerical analysis. Methods. indicated is considering as particular case given boundary nonlinear second order differential equations. For solution formulation there used criterion potentiality operators — symmetry Gateaux derivative ˆ operator problem. This also multiplier and corresponding principle. On constructed investigated discrete analog pendulum. Results. It proved that not potential respect classical bilinear form. There found obtained found. As cases one can deduce from results are performed experiments, establishing dependence solutions change parameters. Conclusion. worked approach two schemes presented simulation under different parameters Numerical show sufficiently amplitude big frequency oscillations point realizes periodical motion.