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The product of the force on an object and the displacement the object undergoes along the direction of the force.
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What does the geometric product between displacement (or maybe position) and force vectors m...
Your observation on work is most closely related to equation (98) in that paper where the power (rate of change of kinetic energy) is found to be $K=V\cdot \tilde W=\omega \cdot \Gamma+v\cdot f$. … These 'splits' are how geometric algebra picks a reference frame to work in. …