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State Space Representation

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...

Space Trusses

Space Trusses

A space truss is a three-dimensional counterpart of a planar truss. These structures consist of members connected at their ends, often utilizing ball-and-socket joints to create a stable and versatile framework. The space truss is widely used in various construction projects due to its adaptability and capacity to withstand complex loads.
At the core of a space truss lies the fundamental unit known as the tetrahedron. This structure is composed of six members that form a three-dimensional shape...

Transfer Function to State Space

Transfer Function to State Space

State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an RLC...

State Space to Transfer Function

State Space to Transfer Function

The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:

Space Trusses: Problem Solving

Space Trusses: Problem Solving

A space truss is a three-dimensional counterpart of a planar truss. These structures consist of members connected at their ends, often utilizing ball-and-socket joints to create a stable and versatile framework. Due to its adaptability and capacity to withstand complex loads, the space truss is widely used in various construction projects.
Consider a tripod consisting of a tetrahedral space truss with a ball-and-socket joint at C. Suppose the height and lengths of the horizontal and vertical...

Rocket Propulsion in Empty Space - I

Rocket Propulsion in Empty Space - I

The driving force for the motion of any vehicle is friction, but in the case of rocket propulsion in space, the friction force is not present. The motion of a rocket changes its velocity (and hence its momentum) by ejecting burned fuel gases, thus causing it to accelerate in the direction opposite to the velocity of the ejected fuel. In this situation, the mass and velocity of the rocket constantly change along with the total mass of ejected gases. Due to conservation of momentum, the...

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Related Experiment Video

Updated: Jan 22, 2026

Simulating the Mechanics of Lens Accommodation via a Manual Lens Stretcher

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Published on: February 23, 2018

In the Intersubjective Space: Hypnosis Through a Neuropsychological Lens.

David S Alter¹

¹a Partners in Healing of Minneapolis , Minnetonka , Minnesota , USA.

The American Journal of Clinical Hypnosis

|July 3, 2019

Summary

This study explores how relationship principles influence attentional focus in clinical hypnosis. Understanding the social brain, trance, and narrative enhances hypnotic practice for adaptive change.

Keywords:

Evolution healing narrative hypnosis hypnosis training neurophysiology neuropsychology

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Area of Science:

Neuroscience
Psychology
Clinical Hypnosis

Background:

Relationship is a fundamental aspect of life, predating human existence.
Recent evolutionary brain structures confer unique neuropsychological abilities on human relationships.
These social brain structures are linked to trance, an innate response to novelty crucial for adaptive learning.

Purpose of the Study:

To explore five interwoven principles of relationship impacting attentional focus in clinical hypnosis.
To connect evolutionary neurobiology with hypnotic phenomena.
To elucidate the role of narrative and co-creation in therapeutic change.

Main Methods:

Review of evolutionary neurobiology and social brain structures.
Exploration of the link between social brain functions and trance.
Conceptual analysis of narrative as a multilevel, embodied concept.
Integration of principles into a framework for clinical hypnosis practice.

Main Results:

Relationship is foundational to attentional focus and hypnotic practice.
Social brain evolution provides a neurobiological basis for trance and hypnotic phenomena.
Narrative is a key, embodied element in the impact of hypnotic interactions.
Hypnosis is framed as a co-creative skill set for facilitating adaptive change.

Conclusions:

Clinical hypnosis effectiveness is enhanced by understanding relationship dynamics.
The integration of neurobiology, trance, and narrative offers a richer framework for hypnosis.
Attuned clinicians can leverage co-creative interaction for client-centered adaptive change.