4.11. Differential Equation
A differential equation can be defined in either implicit or explicit form as follows.
\(\dot{\zeta}=f(\zeta, x, t)\) : Explicit form
\(0=f(\zeta, \dot{\zeta}, x, t)\) : Implicit form
Where \(\zeta\) is the differential variable and x is other state variables. The equation can be expressed as a function expression or as User Written Subroutine. Good initial condition helps to converge in the initial assembly process. Value of the differential variable and its derivative can be referenced by DIF and DIF1.
Expressions or user written subroutines can be utilized to define this element. Variable equation elements are defined by the Differential Equation command in the Subentity menu.
Figure 4.137 Differential Equation List dialog box
No: Shows the number of equations.
Name: Shows the name of equation. You cannot use reserved words in RecurDyn.
Expression: Shows the defined equation.
Comment: Shows the comment of the Differential Equation.
Create: Creates a Differential Equation.
Insert: Inserts a Differential Equation at the current cursor row.
Delete: Deletes a Differential Equation at the current cursor row.
Create or Insert as shown in Figure 4.137 and specify Name and the equation type as shown in Figure 4.138.
Figure 4.138 Differential Equation dialog box
Name: Specifies the name of differential equation.
Function Type: Choose the function type of Explicit or Implicit.
Type: Choose the type of expression as Standard Differential Equation or User Subroutine Equation.
Initial Condition: Specifies the initial conditions.
DIF: Specifies the value of the state variable.
DIF1: Specifies the value of the time derivative of the state variable.
EL: Accesses the Expression List dialog box.
PV: Accesses the Parametric Value dialog box.
Hold to Differential Value during the Static Analysis: If you check this option, this variable equation
Inactive flag: If you check this option, this variable equation becomes inactive.
Note
If this equation is used in the expression of a joint or a force, the error message appears when executing the analysis.
How to use a Differential Equation in an Expression
The user can use a differential equation in an expression as follows:
Dif(difname) and Dif1(difname)
Figure 4.139 Expression using difname
The user can also register the differential equation and refer the differential equation by the register id as follows:
Dif(id) and Dif1(id)
Figure 4.140 Expression using id