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Related Concept Videos

BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.
Oscillations about an Equilibrium Position01:04

Oscillations about an Equilibrium Position

Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so because...
Pole and System Stability01:24

Pole and System Stability

The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's response.
Types of Damping01:20

Types of Damping

If the amount of damping in a system is gradually increased, the period and frequency start to become affected because damping opposes, and hence slows, the back and forth motion (the net force is smaller in both directions). If there is a very large amount of damping, the system does not even oscillate; instead, it slowly moves toward equilibrium. In brief, an overdamped system moves slowly towards equilibrium, whereas an underdamped system moves quickly to equilibrium but will oscillate about...
Stability of Equilibrium Configuration01:23

Stability of Equilibrium Configuration

Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
Dynamic Equilibrium02:20

Dynamic Equilibrium

A reversible chemical reaction represents a chemical process that proceeds in both forward (left to right) and reverse (right to left) directions. When the rates of the forward and reverse reactions are equal, the concentrations of the reactant and product species remain constant over time and the system is at equilibrium. A special double arrow is used to emphasize the reversible nature of the reaction. The relative concentrations of reactants and products in equilibrium systems vary greatly;...

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Related Experiment Video

Updated: Jun 5, 2026

Simulation of Human-induced Vibrations Based on the Characterized In-field Pedestrian Behavior
10:52

Simulation of Human-induced Vibrations Based on the Characterized In-field Pedestrian Behavior

Published on: April 13, 2016

Bouncing between model and data: stability, passivity, and optimality in hybrid dynamics.

Renaud Ronsse1, Dagmar Sternad

  • 1Biorobotics Laboratory, Institute of Bioengineering, École Polytechnique Fédérale de Lausanne, Switzerland.

Journal of Motor Behavior
|December 25, 2010
PubMed
Summary
This summary is machine-generated.

Understanding coordinative behavior in ball bouncing requires analyzing racket-ball interactions. New models integrate passive and active control strategies for improved performance prediction.

Related Experiment Videos

Last Updated: Jun 5, 2026

Simulation of Human-induced Vibrations Based on the Characterized In-field Pedestrian Behavior
10:52

Simulation of Human-induced Vibrations Based on the Characterized In-field Pedestrian Behavior

Published on: April 13, 2016

Area of Science:

  • Motor control
  • Human-robot interaction
  • Dynamical systems theory

Background:

  • Ball bouncing involves complex coordinative behavior, requiring perception and adaptation.
  • Existing models analyze racket-ball dynamics but struggle with fine-grained performance prediction.

Purpose of the Study:

  • Investigate control strategies in rhythmic ball bouncing.
  • Develop and test models of coordinative behavior.
  • Reconcile passive and active control mechanisms.

Main Methods:

  • Developed dynamical models of racket-ball interactions.
  • Conducted experimental studies with perturbations.
  • Analyzed stability and control strategies using model-based hypotheses.

Main Results:

  • Passive stability observed through negative acceleration impacts.
  • Active, perceptually guided corrections enhance recovery from perturbations.
  • Initial active control models captured some trajectory features but lacked fine-grained accuracy.

Conclusions:

  • Rhythmic ball bouncing utilizes both passive stability and active control.
  • A novel model integrating these approaches shows promise for predicting fine-grained behavior.
  • Future experiments will test new model predictions.