#multivector

[peeterjoot]

Multivector form of Leibniz integral theorem for line integrals.

[Click here for a PDF version of this post] Goal. Here we will explore the multivector form of the Leibniz integral theorem (aka. Feynman’s trick in one dimension), as discussed in [1]. Given a boundary \( \Omega(t) \) that varies in time, we seek to evaluate \begin{equation}\label{eqn:LeibnizIntegralTheorem:20} \ddt{} \int_{\Omega(t)} F d^p \Bx \lrpartial G. \end{equation} Recall that when the…

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[peeterjoot]

Multivector Lagrangian for Maxwell's equation.

Multivector Lagrangian for Maxwell’s equation.

This is the 5th and final part of a series on finding Maxwell’s equations (including the fictitious magnetic sources that are useful in engineering) from a Lagrangian representation. [Click here for a PDF version of this series of posts, up to and including this one.]  The first, second, third and fourth parts are also available here on this blog. We’ve found the charge and currency dependency…

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[peeterjoot]

A derivation of the quaternion Maxwell's equations using geometric algebra.

A derivation of the quaternion Maxwell’s equations using geometric algebra.

[Click here for a PDF of this post with nicer formatting]

Motivation.

The quaternion form of Maxwell’s equations as stated in [2] is nearly indecipherable. The modern quaternionic form of these equations can be found in [1]. Looking for this representation was driven by the question of whether or not the compact geometric algebra representations of Maxwell’s equations \( \grad F = J \), was…

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[verainacio]