# Bulletin of the American Physical Society

# 18th Biennial Intl. Conference of the APS Topical Group on Shock Compression of Condensed Matter held in conjunction with the 24th Biennial Intl. Conference of the Intl. Association for the Advancement of High Pressure Science and Technology (AIRAPT)

## Volume 58, Number 7

## Sunday–Friday, July 7–12, 2013; Seattle, Washington

### Session M1: Poster Session II (5:30 - 7:00PM)

5:30 PM,
Tuesday, July 9, 2013

Room: Grand Ballroom I

Abstract ID: BAPS.2013.SHOCK.M1.21

### Abstract: M1.00021 : Angle-Distortion Equations in Special Relativity

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#### Author:

Florentin Smarandache

(The University of New Mexico)

Let's consider an object of triangular form $\Delta $\textit{ABC }moving in the direction of its bottom base \textit{BC} (on the $x-$axis), with speed $v$. The side \textit{\textbar BC\textbar }$= \quad \alpha $\textit{ is} contracted with the Lorentz contraction factor $C(v)=\sqrt {1-v^{2}/c^{2}} $ since \textit{BC} is moving along the motion direction, therefore \textit{\textbar B'C'\textbar }$= \quad \alpha C(v). $But the oblique sides \textit{AB }and \textit{CA} are contracted respectively with the oblique-contraction factors \textit{OC(v, B) }and\textit{ OC(v, }$\pi -C),$ where the \textbf{oblique-length contraction factor} is defined as: \[ OC(v,\theta )=\sqrt {C(v)^{2}\cos^{2}\theta +\sin^{2}\theta } . \] In the resulting triangle $\Delta A'B'C'$ one simply applies the Law of Cosine in order to find each distorted angle A', B', and C'. Therefore: \[ A'=\arccos \frac{-\alpha^{2}\cdot C(v)^{2}+\beta^{2}\cdot OC(v,A+B)^{2}+\gamma^{2}\cdot OC(v,B)^{2}}{2\beta \cdot \gamma \cdot OC(v,B)\cdot OC(v,A+B)}, \] \[ B'=\arccos \frac{\alpha^{2}\cdot C(v)^{2}-\beta^{2}\cdot OC(v,A+B)^{2}+\gamma^{2}\cdot OC(v,B)^{2}}{2\alpha \cdot \gamma \cdot C(v)\cdot OC(v,B)}, \] \[ C'=\arccos \frac{\alpha^{2}\cdot C(v)^{2}+\beta^{2}\cdot OC(v,A+B)^{2}-\gamma^{2}\cdot OC(v,B)^{2}}{2\alpha \cdot \beta \cdot C(v)\cdot OC(v,A+B)}. \] The angles A', B', and C' are, in general, different from the original angles$ A, B, $and $ C$ respectively. The distortion of an angle is, in general, different from the distortion of another angle.

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2013.SHOCK.M1.21

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