# 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

- Model configuration.
- Static equilibrium configuration.
- 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

- 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.