The differential time operator was decoupled from any

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Unformatted text preview: orthogonal, then x xR R iff .R The scalar term is not zero. What this implies is not yet clear, but it may be related to the fact that the frame is not inertial. Implications Three forms of Newton’s second law were generated by choosing appropriate operator quaternions acting on position quaternions. The differential time operator was decoupled from any differential space operators. This may be viewed as an operational definition of ”classical” physics. 2 ¡ ¡1  .R x xR ¡ ¡1  ¡ ¡ ¡1  .R , R xR R ¡1 ¢ ¡ ¡1 ¡ ¡1 ¡1 ¡1 ¢ ¡ . ¢ d , dt xR . 2 xR . ¡ ¡1 . .R , R ¢ ¡ ¡ d , dt xR .R 0 ¡ ¡1 . .R , R ¡ ¡ ¡1 ¡ ¡1 ¢ £¡ ¢ ¡1 ¡1 ¡ ¡1 ¡1 ¡ ¡1 ¢ ¡1 ¢ ¡1 2 2 Oscillators and Waves A professor of mine once said that everything in physics is a simple harmonic oscillator. Therefore it is necessary to get a handle on everything. The Simple Harmonic Oscillator (SHO) The differential equation for a simple harmonic oscillator in one dimension can be express with quate...
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This note was uploaded on 09/30/2010 for the course MAE 123 taught by Professor 123 during the Spring '10 term at École Normale Supérieure.

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