It looks as if the EM drive might work. A NASA Eagleworks paper has appeared
now on November 17. The drive produces a thrust apparently violating momentum
conservation. However, as the effect appears to be quantum mechanical this
is not necessarily a contradiction. The drive could make use of the fact that
vaccum is not really empty.
As for applications, NASA is interested in that since the drive could be used
for deep space missions.
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From the paper:
"Measurement of Impulsive Thrust from a Closed Radio-Frequency Cavity in Vacuum",
published on November 17, 2016, by
Harold White, Paul March, James Lawrence, Jerry Vera, Andre Sylvester,
David Brady, and Paul Bailey.
It was previously reported that radio-frequency (RF) resonant
cavities generated anomalous thrust on a low-thrust torsion
pendulum [1,2] in spite of the apparent lack of a propellant or other
medium with which to exchange momentum. It is shown here that a
dielectrically loaded, tapered RF test article excited in the transverse
magnetic 212 (TM212) mode (see Fig. 1) at 1937 MHz is capable of
consistently generating force at a thrust-to-power level of 1.2 +/i 0.1 mN/kW
with the force directed to the narrow end under vacuum conditions.
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As for multivariable calculus: look at the paper. Here is a graph from that
paper featuring some vector fields:
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