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Unformatted text preview: m ) ) && 2 d2 x dt2 ) () %&& ©¦ ©¦ ¡ ¡ 0 %&& && ' %&& && ' ¢ ¢ ¢ Implications
Using the appropriate combinations of quaternion operators, the classical simple harmonic oscillator and wave equation were written out and solved. The functional deﬁnition of classical physics employed here is that the time operator is decoupled from any space operator. There is no reason why a similar combination of operators cannot be used when time and space operators are not decoupled. In fact, the four Maxwell equations appear to be one nonhomogeneous quaternion wave equation, and the structure of the simple harmonic oscillator appears in the Klein-Gordon equation. 4 3 Four Tests for a Conservative Force
There are four well-known, equivalent tests to determine if a force is conservative: the curl is zero, a potential function whose gradient is the force exists, all closed path integrals are zero, and the path integral between any two points is the same no matter what the path chosen. In this notebook, quaternion opera...
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- Spring '10