# Linear Simulation

General multibody systems are almost always nonlinear. Nonlinearities may arise from force elements with nonlinear constitutive relations, constraints, or kinematics. In general, nonlinear systems are notoriously difficult to analyze. You may find it useful to study linearized versions of your models created using MotionSolve.

MotionSolve provides the following two types of results based on linearized equations.

## Eigensolution for Stability and Vibration Analysis

Your model can be linearized about an arbitrary configuration which can be defined in one of the following three ways:
1. Model configuration.
2. Static equilibrium configuration.
3. Configuration at the end of transient simulation.

MotionSolve linearizes your model and calculates the eigenvalues and normal modes. The eigenvalues predict stability and natural frequencies of vibration modes. The normal modes help you understand the motion patterns of vibrating systems.

## Linearized Plant Model for Control System Design

Another common reason to do linearization is to obtain a simplified model of your system for the purpose of control system design. This is done by specifying the inputs to and outputs from your mechanical system, and using MotionSolve to generates the state space description of the system (plant) in the following form: (1)
$\begin{array}{l}\stackrel{˙}{x}=Ax+Bu\\ y=Cx+Du\end{array}$
The set of inputs and outputs can be defined using the Control_PlantInput and Control_PlantOutput modeling elements, respectively. The Param_Linear command element triggers the linearization solution, which produces the following results:
• Matrices A, B, C, and D are written in Matlab format, in four separate files, with the extensions *.a, *.b, *.c, and *.d, respectively.
• The state space form linear system is written in Simulink format in an .mdl file.
• States selected for linearization are written out to a *.tag file.
• Eigenvalues are written to the *.eig file.
• Eigenvectors and eigenvalues are written out in tabular format to the *.tab file.
• One MRF file is written per eigenvector. It is used for mode shape animation in conjunction with the MotionView model MDL file. Note that this is a different file than the Simulink MDL file.