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Alternative Sets of Equilibrium Equations

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When analyzing the behavior of structures, engineers often rely on the concept of equilibrium. This refers to the state where all forces and moments acting on a system balance each other, resulting in no net movement or rotation. In many cases, equilibrium can be described by a set of standard equations. However, in some situations, alternative sets of equilibrium equations must be used to describe the system's behavior accurately.
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Related Experiment Video

Updated: Jun 28, 2026

New Variations for Strategy Set-shifting in the Rat

New Variations for Strategy Set-shifting in the Rat

Published on: January 23, 2017

The RAMESES algorithm for multiple equilibria-IV. Strategies for improvement (RAMESES III).

B W Darvell¹, V W Leung

¹Dental Materials Science Unit, University of Hong Kong, Prince Philip Dental Hospital, 34 Hospital Road, Hong Kong.

|August 1, 1991

Summary

The RAMESES algorithm was improved using the dynamically adaptive extrapolation procedure (ADEPT) for more accurate chaotic behavior control. Enhanced speed was achieved through optimized array addressing, improving computational efficiency.

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Last Updated: Jun 28, 2026

New Variations for Strategy Set-shifting in the Rat

New Variations for Strategy Set-shifting in the Rat

Published on: January 23, 2017

Area of Science:

Computational Mathematics
Numerical Analysis
Algorithm Development

Background:

The RAMESES algorithm requires enhanced accuracy and efficiency for complex problems.
Chaotic behavior in feedback systems presents significant computational challenges.

Purpose of the Study:

To improve the RAMESES algorithm's accuracy and speed.
To control chaotic behavior in systems with exaggerated feedback.
To introduce a dynamically adaptive extrapolation scheme.

Main Methods:

Enhanced forward extrapolation procedure using a smoothed polynomial function.
Implementation of a dynamically adaptive extrapolation procedure (ADEPT).
Limiting correction factors to control chaotic behavior.
Indirect addressing of sparse array elements for speed optimization.

Main Results:

More accurate estimates achieved through the smoothed polynomial function in ADEPT.
Successful control of chaotic behavior by limiting correction factors.
Significant improvement in execution speed via indirect addressing.
Illustrative examples demonstrating the algorithm's effectiveness.

Conclusions:

The enhanced RAMESES algorithm with ADEPT offers improved accuracy and computational efficiency.
The method effectively controls chaotic dynamics in feedback systems.
The optimizations provide a robust solution for complex computational problems.