Difference between revisions of "Function Conjunction"

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==The Anatomy of a Physical Expression==
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{{#seo:
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|title=Function Conjunction @ Sho Drives Wiki
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|keywords=electricity,magnetism,motor,generator
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|description=To facilitate understanding of the S.H.O. Drive, this place catalogs the ideas, creations, and techniques underlying its invention.
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}}
  
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{| class="wikitable"
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To facilitate understanding of the S.H.O. Drive, this '''Function Conjunction''' will catalog the ideas, creations, and techniques underlying its invention.
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! Constant
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! Coefficient
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! Quantity
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! Proximity
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! Dislocation
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! Direction
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|valign=top| '''Examples:'''<br><math>\mu_0, \epsilon_0</math><br><math>k_B, \alpha, c</math>
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|valign=top| '''Examples:'''<br><math>\mu_r, \epsilon_r</math><br><math>N</math>
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|valign=top| '''Examples:'''<br><math>q,\lambda_q,\sigma_q,\rho_q</math><br><math>m,\rho</math>
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|valign=top| '''Examples:'''<br><math>\frac{1}{|\mathbf{r}|}, \frac{1}{|\mathbf{r}|^2}</math>
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|valign=top| '''Examples:'''<br><math>\mathbf{r}, \frac{d\mathbf{r}}{dt}, \frac{d^2\mathbf{r}}{dt^2}</math><br><math>\mathbf{r'}, \frac{d\mathbf{r'}}{dt}, \frac{d^2\mathbf{r'}}{dt^2}</math><br><math>\mathbf{x}, \mathbf{v}, \mathbf{a}, \beta</math>
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|valign=top| '''Examples:'''<br><math>\mathbf{\hat{r}},\mathbf{\hat{\dot{r}}},\mathbf{\hat{\ddot{r}}}</math><br><math>\mathbf{\hat{r'}},\mathbf{\hat{\dot{r'}}},\mathbf{\hat{\ddot{r'}}}</math><br><math>\mathbf{\hat{x}}, \mathbf{\hat{v}}, \mathbf{\hat{a}}</math>
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===Constants===
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'''[[Magnetic Energy]]'''
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* <math>\mu_0</math> = Magnetic Permeability of Free Space
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* <math>\epsilon_0</math> = Electric Permittivity of Free Space
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* <math>k_B</math> = Boltzmann's constant
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* <math>\alpha</math> = Fine Structure Constant
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* <math>c</math> = Speed of Light
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===Quantities===
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: The Magnetic Energy is the energy existing in magnetic fields.
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* <math>q</math> = point charge
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* <math>\lambda_q</math> = linear charge density (for continuous charge)
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* <math>\sigma_q</math> = surface charge density (for continuous charge)
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* <math>\rho_q</math> = volume charge density (for continuous charge)
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* <math>m</math> = mass
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* <math>\rho</math> = volume mass density
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===Dislocations===
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'''[[The Anatomy of a Physical Expression]]'''
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* <math>\mathbf{r'}</math> = position at which a light signal is emitted at the retarded time <math>t' = t - |\mathbf{r}-\mathbf{r'}|/c</math>
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* <math>\frac{d\mathbf{r'}}{dt}</math> = velocity of the source of the light signal at the retarded time <math>t' = t - |\mathbf{r}-\mathbf{r'}|/c</math>
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* <math>\frac{d^2\mathbf{r'}}{dt^2}</math> = acceleration of the source of the light signal at the retarded time <math>t' = t - |\mathbf{r}-\mathbf{r'}|/c</math>
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==Functions Composed of Physical Expressions==
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: A physical expression is a product of factors, each with their own distinct role in defining a property of a physical system. Types include constants, coefficients, quantities, proximities, dislocations, and directions.
  
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===Electric scalar potential <math>\mathbf{\varphi}</math>===
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'''[[Functions composed of Physical Expressions]]'''
  
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''<math>\mathbf{\varphi}</math> of a point charge <math>q</math>'':
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: A function composed of physical expressions is simply the result of the summations, differences, exponentiations, logarithms, or distributed multiplications or divisions of these physical expressions, or in the simplest case, a function is simply equal to an expression, such as <math>E(m) = mc^2</math>, where <math>E</math> is a function of <math>m</math>.
  
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<math>\mathbf{\varphi}\left(\mathbf{r},\mathbf{r'}\right) = \underset{constant}{\frac{q}{4\pi\ \epsilon_0}} \times \underset{proximity}{\frac{1}{|\mathbf{r}-\mathbf{r'}|}}</math>
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'''[[Electromagnetic Potentials]]'''
  
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===Magnetic vector potential <math>A</math>===
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: The basic idea here is that the electromagnetic potentials <math>\phi</math> and <math>A</math> and their derivatives can be used to derive all electromagnetism.
  
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''<math>\mathbf{A}</math> of a moving point charge <math>q</math>'':
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{{Site map}}
  
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<math>\mathbf{A}\left(\mathbf{r},\mathbf{r'},\mathbf{v}\right) = \underset{constant}{\frac{\mu_0\ q}{4\pi}} \times \underset{proximity}{\frac{1}{|\mathbf{r}-\mathbf{r'}|}} \times \underset{dislocation}{\mathbf{v}}</math>
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[[Category:Function Conjunction| ]]

Latest revision as of 19:22, 14 July 2017

To facilitate understanding of the S.H.O. Drive, this Function Conjunction will catalog the ideas, creations, and techniques underlying its invention.

Magnetic Energy

The Magnetic Energy is the energy existing in magnetic fields.

The Anatomy of a Physical Expression

A physical expression is a product of factors, each with their own distinct role in defining a property of a physical system. Types include constants, coefficients, quantities, proximities, dislocations, and directions.

Functions composed of Physical Expressions

A function composed of physical expressions is simply the result of the summations, differences, exponentiations, logarithms, or distributed multiplications or divisions of these physical expressions, or in the simplest case, a function is simply equal to an expression, such as [math]E(m) = mc^2[/math], where [math]E[/math] is a function of [math]m[/math].

Electromagnetic Potentials

The basic idea here is that the electromagnetic potentials [math]\phi[/math] and [math]A[/math] and their derivatives can be used to derive all electromagnetism.

Site map

HQ ● Glossary ● April 2016 Presentation

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