Example for Differential Equation

 

Decription for example model

 

The user can model differential equations for model such as spring system using DE.

Figure 1  Example model

 

The differential equation for the above example model is as follows:

 

The model is defined as following equation.

 

And transform 2nd order differential equation to 1st order one.

 

And modify to general matric form.

 

RecurDyn model for varification

 

Compare the two results by creating a model using differential equations and a verification model using dynamics.

 

Figure 2  Differential equation model and verification model using dynamics

 

Differential equation_1 (Using explicit form)

 

The user can define a differential equation in an explicit form.

 

The equation using explicit form is following:

 

Set the PV, VE, DE and Expression like as following:

 

Figure 3  Set PV

 

Figure 4  Set VE

 

Figure 5  Set DE

 

Figure 6  Set Expression

 

 

Differential equation_2 (Using implicit form)

 

The user can define a differential equation in an implicit form.

 

The equation using implicit form is following:

 

 

Set the PV, VE, DE and Expression like as following:

 

Figure 7  Set PV

 

Figure 8  Set VE

 

Figure 9  Set DE

 

Figure 10  Set Expression

 

Results of differential equation

 

Figure 8  Comparison of differential equation results and dynamic analysis results