WOLFRAM SYSTEM MODELER

InitSpringConstant

Determine spring constant such that system is in steady state at given position

Diagram

Wolfram Language

In[1]:=
SystemModel["Modelica.Mechanics.MultiBody.Examples.Elementary.InitSpringConstant"]
Out[1]:=

Information

This information is part of the Modelica Standard Library maintained by the Modelica Association.

This example demonstrates a non-standard type of initialization by calculating a spring constant such that a simple pendulum is at a defined position in steady state.

The goal is that the pendulum should be in steady state when the rotation angle of the pendulum is zero. The spring constant of the spring shall be calculated during initialization such that this goal is reached.

The pendulum has one degree of freedom, i.e., two states. Therefore, two additional equations have to be provided for initialization. However, parameter "c" of the spring component is defined with attribute "fixed = false", i.e., the value of this parameter is computed during initialization. Therefore, there is one additional equation required during initialization. The 3 initial equations are the rotational angle of the revolute joint and its first and second derivative. The latter ones are zero, in order to initialize in steady state. By setting the start values of phi, w, a to zero and their fixed attributes to true, the required 3 initial equations are defined.

After translation, this model is initialized in steady-state. The spring constant is computed as c = 49.05 N/m. An animation of this simulation is shown in the figure below.

model Examples.Elementary.InitSpringConstant

Components (6)

world

Type: World

Description: World coordinate system + gravity field + default animation definition

rev

Type: Revolute

Description: Revolute joint (1 rotational degree-of-freedom, 2 potential states, optional axis flange)

damper

Type: Damper

Description: Linear 1D rotational damper

body

Type: BodyShape

Description: Rigid body with mass, inertia tensor, different shapes for animation, and two frame connectors (12 potential states)

fixed

Type: Fixed

Description: Frame fixed in the world frame at a given position

spring

Type: Spring

Description: Linear translational spring with optional mass