Energy Cost of Dynamical Stabilization: Stored versus Dissipated Energy
Armen E Allahverdyan1,2, Edvard A Khalafyan3
1Alikhanian National Laboratory, Yerevan Physics Institute, 2 Alikhanian Brothers Street, Yerevan 0036, Armenia.
Entropy (Basel, Switzerland)
|July 27, 2022
Summary
Dynamical stabilization, or homeostasis, can be achieved in systems like Kapitza's pendulum with transient energy dissipation, not necessarily constant energy cost. This study explores energy resources for maintaining stable states.
Area of Science:
- Physics
- Control Theory
- Dynamical Systems
Background:
- Homeostasis is essential in nature but its energy costs are understudied.
- Kapitza's pendulum is a well-known model for control studies.
Purpose of the Study:
- To systematically investigate the energetic resources required for dynamical stabilization.
- To analyze energy dissipation in stabilizing normally unstable states.
Main Methods:
- Generalizing and rendering autonomous the Kapitza pendulum model.
- Analyzing the effects of friction and stored energy on stability.
- Investigating conditions for asymptotic stability and energy dissipation.
Main Results:
- Friction and stored energy can stabilize the upper, unstable state of the pendulum.
- Asymptotic stability is achievable with only transient energy dissipation in some cases.
- Constant energy dissipation may be required for stabilization in other regimes.
Conclusions:
- Dynamical stabilization does not always require constant energy dissipation.
- The energy cost of homeostasis depends on system parameters and perturbation types.
- Understanding energy decay mechanisms is crucial for dynamically stabilized states.
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