Mathematical modeling analysis and verification of vibration isolation parts of washing machine

Washing machines are used very frequently in everyday life. There have been many related studies on the vibration and noise of washing machines. The suspension system is an important vibration isolation component of the washing machine. Based on the Lagrangian equation, the dynamic model of the suspension system was established. The reliability of the model was verified by finite element simulation and experimental methods. Finally, this paper used a multi-objective optimization method to obtain optimal parameters of the washing machine and further to reduce the vibration level of washing machines.

Tunneling under the influence of quantum gravity in black rings

We explore the Lagrangian equation in the background of generalized uncertainty principle. The tunneling radiation through the black ring horizon is observed. We investigated the tunneling radiation through the Hamilton–Jacobi method for solutions of Einstein–Maxwell-dilation gravity theory. The radiation of black ring without back reaction and self-interaction of particles are studied. Furthermore, we consider the quantum gravity effect on the stability of black ring.

Stability Analysis of an Inverted Pendulum on a Cart with the Presence of Restoring and Frictional Forces Disturbance using Observer Based and Full State Feedback H2 Controllers

In this paper, the stability control of the inverted pendulum on a cart with a disturbance forces has been done using observer based and full state feedback H2 controllers. The Lagrangian equation has been used to model the system equation of motions and linearized the system to the unstable upward position. Comparison of the system stability has been simulated by comparing the proposed controllers using Matlab/Scripts and a promising results has been analyzed successfully.

Stability Analysis of an Inverted Pendulum on a Cart with the Presence of Restoring and Frictional Forces Disturbance using Observer Based and Full State Feedback H2 Controllers

In this paper, the stability control of the inverted pendulum on a cart with a disturbance forces has been done using observer based and full state feedback H2 controllers. The Lagrangian equation has been used to model the system equation of motions and linearized the system to the unstable upward position. Comparison of the system stability has been simulated by comparing the proposed controllers using Matlab/Scripts and a promising results has been analyzed successfully.

The Degenerate Special Lagrangian Equation on Riemannian Manifolds

We show that the degenerate special Lagrangian equation (DSL), recently introduced by Rubinstein–Solomon, induces a global equation on every Riemannian manifold, and that for certain associated geometries this equation governs, as it does in the Euclidean setting, geodesics in the space of positive Lagrangians. For example, geodesics in the space of positive Lagrangian sections of a smooth Calabi–Yau torus fibration are governed by the Riemannian DSL on the base manifold. We then develop their analytic techniques, specifically modifications of the Dirichlet duality theory of Harvey–Lawson, in the Riemannian setting to obtain continuous solutions to the Dirichlet problem for the Riemannian DSL and hence continuous geodesics in the space of positive Lagrangians.