Difference between revisions of "Function Conjunction"

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==The Anatomy of an 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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|}
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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 of a charge <math>q</math> at time <math>t</math>, when it receives a light signal from <math>q'</math> that was emitted earlier at time <math>t' = t - |\mathbf{r}-\mathbf{r'}|/c</math>
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* <math>\frac{d\mathbf{r}}{dt}</math> = velocity of a charge <math>q</math> at time <math>t</math>, when it receives a light signal from <math>q'</math> that was emitted earlier at 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 a charge <math>q</math> at time <math>t</math>, when it receives a light signal from <math>q'</math> that was emitted earlier at time <math>t' = t - |\mathbf{r}-\mathbf{r'}|/c</math>
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* <math>\mathbf{r'}</math> = position a charge <math>q'</math> was at the retarded time <math>t' = t - |\mathbf{r}-\mathbf{r'}|/c</math>, when it emitted a light signal which has now reached <math>q</math> at position <math>\mathbf{r}</math> and time <math>t</math>
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* <math>\frac{d\mathbf{r'}}{dt}</math> = velocity a charge <math>q'</math> was at the retarded time <math>t' = t - |\mathbf{r}-\mathbf{r'}|/c</math>, when it emitted a light signal which has now reached <math>q</math> at position <math>\mathbf{r}</math> and time <math>t</math>
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* <math>\frac{d^2\mathbf{r'}}{dt^2}</math> = acceleration a charge <math>q'</math> was at the retarded time <math>t' = t - |\mathbf{r}-\mathbf{r'}|/c</math>, when it emitted a light signal which has now reached <math>q</math> at position <math>\mathbf{r}</math> and time <math>t</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> at <math>\left(\mathbf{r},t\right)</math>, due to a point charge <math>q'</math> at <math>\left(\mathbf{r'},t'\right)</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{q'}{4\pi\ \epsilon}} \times \underset{proximity}{\frac{1}{|\mathbf{r}-\mathbf{r'}|}} \times \underset{dislocation}{\mathbf{v}/c^2} = \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 E(m)=mc2, where E is a function of m.

Electromagnetic Potentials

The basic idea here is that the electromagnetic potentials ϕ and A and their derivatives can be used to derive all electromagnetism.

Site map

HQ ● Glossary ● April 2016 Presentation

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