# Matlab solution of dynamic equation of sealed rotor system with gear meshing characteristics

The above characteristics of MATLAB make it have a strong advantage in solving differential equations. It provides seven kinds of commands to solve differential equations. For the dimensionless dynamic equations in this paper, in order to ensure sufficient accuracy and calculation efficiency, the ode45 solver with high accuracy is selected to solve the differential equations.

When using MATLAB to solve the higher-order differential equation, we must first transform the higher-order differential equation into a first-order differential equation system to solve it. The transformation principle is as follows:

The kinetic equation is as follows

Where x, m, C, K and f represent displacement vector, mass matrix, damping matrix, stiffness matrix and load vector respectively.

It can be transformed into the following form:

Let x = IX, I be the identity matrix of the same order as m, then the above formula can be written as follows:

For the first derivative, the above formula can be transformed into:

After the above transformation, the equation is transformed from the original n-dimensional second-order differential equation to the 2n dimensional first-order differential equation. At this time, the numerical integration method can be used and MATLAB software is used to write the program to solve the equation.

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