What is a Dynamically Stiff System?

The motion of certain physical systems is inherently difficult to compute. A large category of such systems is termed Dynamically Stiff Systems. Some scenarios responsible for a Dynamically Stiff System are:

1. Small masses attached to relatively stiff springs or dampers.

Because the natural frequency, , of a spring-mass system is defined by:

where k = spring constant
m = mass

a large ratio will result in high frequency vibrations.

Analogously, a large ratio (where c is the damping coefficient) will yield a Dynamically Stiff System when dampers are involved.

2. Different bodies moving at very different rates.

If some bodies in a simulation are moving very slow while others are moving very fast, the system's motion as a whole is very hard to compute.

Connecting bodies of substantially different mass will often result in very large differences in motion between the two connected bodies. When bodies are connected through a constraint, an equal but opposite force is applied to each body by that constraint, as governed by Newton's 3^rd Law of Motion. These forces, though equal in magnitude, yield vastly different accelerations of the two bodies (due to their substantially different masses).

3. Rapidly changing forces or accelerations.

Friction can yield rapidly changing forces (and hence accelerations). Because the force of friction always opposes motion, a frictional force can change instantaneously from a positive value to a negative value (without any change in magnitude, ) when the velocity of the object changes direction.

Formulas (particularly ones containing If( ) statements) written into the value field of WM3D Forces, Linear Actuators, Torques, or Revolute Motors may yield forces and/or accelerations whose rapid variance causes difficulties.

4. Tight error tolerances.

A Dynamically Stiff System can result if the error tolerances set within the Simulation Accuracy dialog (How should Simulation Accuracy settings be modified?) are set exceedingly small. The default settings will never yield such results.

WM3D may respond to Dynamically Stiff Systems by issuing any of the following warning messages:

Unable to Achieve desired Accuracy with Variable Time Step Integration

Inconsistent Constraints / Physical Instabilities

Some Forces are Large

Torna alla pagina di supporto

Versioni pertinenti:

Data ultimo aggiornamento: 2 settembre 2011

Lista Studio srl®
URL : http://www.simwise4d.it
diritti riservati, riproduzione vietata