AAWSAP DIRD, Negative Mass Propulsion, January 2011

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UNCLASSIFIED//FOR OFFICIAL USE ONLY

$$
F = m \left[ \hat{\mathbf{E}} + \frac{1}{c} \mathbf{v} \times \hat{\mathbf{H}} \right], \qquad (87)
$$

where

$$
\hat{\mathbf{E}} = \frac{\partial \mathbf{v}}{\partial t} + \mathbf{curl} \times \mathbf{r} - \mathbf{omega} \times (\mathbf{omega} \times \mathbf{r})
$$

$$
\hat{\mathbf{H}} = -2c\mathbf{omega}. \qquad (88)
$$

With

$$
curl(\mathbf{omega} \times \mathbf{r}) = 2\mathbf{omega}
$$

$$
div(-\mathbf{omega} \times (\mathbf{omega} \times \mathbf{r})) = 2\mathbf{omega}^2, \qquad (89)
$$

one has

$$
div \hat{\mathbf{H}} = 0
$$

$$
\frac{1}{c} \frac{\partial \hat{\mathbf{H}}}{\partial t} + curl \hat{\mathbf{E}} = 0. \qquad (90)
$$

$\hat{\mathbf{E}}$ and $\hat{\mathbf{H}}$ can be derived from a scalar and vector potential

$$
\hat{\mathbf{E}} = -\frac{1}{c} \frac{\partial \hat{\mathbf{A}}}{\partial t} - grad \Phi
$$

$$
\hat{\mathbf{H}} = curl \hat{\mathbf{A}}. \qquad (91)
$$

Applied to a rotating reference system one has

$$
\hat{\Phi} = -\frac{1}{2}(\mathbf{omega} \times \mathbf{r})^2 \qquad (92)
$$

$$
\hat{\mathbf{A}} = -c(\mathbf{omega} \times \mathbf{r})
$$

UNCLASSIFIED//FOR OFFICIAL USE ONLY

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