A variable equation represents a variable using scalar algebraic equation created through Function Expression or User Subroutine. Variable equations create an additional governing equation and introduce a new system variable within the Motion solver. Moreover, these variable equations can be integrated into other function expressions using the VARVAL function and incorporated into user subroutine functions through the SYSFNC function.
A Variable Equation defines a scalar variable which may be dependent on the other system variables of the Motion solver as follows.
 | (8–88) |
where:
α = variable equation. This is an equation that
is a function of  ,  ,  ,  ,  ,  ,  ,  ,  and  . |
 = generalized coordinates, which generally refer to variables
corresponding to positions |
 = time derivatives of the generalized coordinates, which
generally refer to variables corresponding to velocities |
 = second time derivatives of the generalized coordinates,
which generally refer to variables corresponding to accelerations |
 ,  ,  ,  = variables of other equations |
 = forces |
 = torques |
 = time |
If the variable equation is dependent on itself, the Motion solver may fail. To ensure an accurate solution, the equation is solved simultaneously with other system variables, which it is allowed to depend on. Variable Equations are not considered in position, velocity, and eigenvalue analysis, but are solved in acceleration, static, and dynamic analysis. If the variable is used in motion during position or velocity analysis, the initial condition will be used.
The variable value is reported in the Motion Postprocessor as shown in the table below.
Figure 8.122: Definition of Variable Equation outputs
| Parameter | Symbol | Description | Dimension |
| Alpha | α | The variable value which is defined in Equation 8–61. | N/A |