# Analysis in MotionSolve

Six basic types of analyses are available in multi-body systems (MBS).

Depending on the characteristics of the problem, a particular set of analyses is performed. Each of these analyses provides different information about the system. More complex analyses can be synthesized by using a combination of these basic analyses.

- Assembly analysis
- Ensures that a complex MBS system is "put-together" correctly, satisfies all the system constraints, and that the system states have the right initial velocities for a subsequent simulation.
- Kinematic analysis
- Simulates the motion of a system that has zero degrees of freedom. The system moves because some of its constraints have an explicit dependence on time. It allows the engineer to determine the range of possible values for the displacement, velocity, and acceleration of any point of interest on a mechanical device. If the mass and inertial properties of the parts are specified, MBS software can also calculate the corresponding applied and reaction forces resulting from the prescribed motions. These calculations are all algebraic in nature. Typical applications of the kinematic analysis include the design of a mechanism and preliminary design of subsystems such as suspensions.
- Static equilibrium analysis
- Determines a state for a system in which all of the internal and external forces are balanced in the absence of any system motion or inertia forces. The principle of virtual work is used to formulate the problem. When the system velocities and accelerations are set to zero, this implies that the sum of the internal and applied forces in all directions is zero. The static equilibrium analysis is typically used to find a starting point for a dynamic analysis by removing unwanted system transients at the start of the simulation. Unbalanced forces in the initial configuration can generate undesirable effects in the dynamic analysis.
- Quasi-static analysis
- A sequence of static analyses performed for different configurations of the system (in contrast to static equilibrium, which is computed at fixed points in time during a simulation). Typical uses of quasi-static analysis include determining the coordinates of hard-points during the development of automotive suspensions and determining the angle of tilt when a forklift can topple over.
- Dynamic analysis
- Provides the time-history solution for all of the displacements, velocities, accelerations, and internal reaction forces in a mechanical system in response to a set of environmental forces and excitations. The governing equations for such an analysis are typically nonlinear, ordinary second order differential-algebraic equations (DAE), which define the force balance conditions. The equations are nonlinear and cannot be solved symbolically. Numerical integrators are used to calculate the solution.
- Linear analysis
- The system nonlinear equations are linearized about an operating point. Two different types of linear analyses, eigenanalysis and state matrix calculations can be performed. Eigenanalysis is the calculation of eigenvalues and eigenvectors for the linearized system. The eigenvalues are the natural frequency/damping characteristics of the system while the eigenvectors represent the modes of the vibration associated with each frequency. Both the eigenvalues and the eigenvectors are complex valued. The state matrices that can be generated from the linearized system are the coefficient matrices for representing a linearized mechanical system in state-space form.