Я использую латекс на своем веб-сайте Moodle. У меня проблема с MathJax. Он показывает первый параметр каждого уравнения дважды (в основном левая часть оператора равенства =). Я использую следующий код:
<p><span id="docs-internal-guid-618520b2-7fff-707e-1f90-60e30cf92cc1"></span></p>
<p style="font-weight: bold; text-align: center;"><b id="docs-internal-guid-618520b2-7fff-707e-1f90-60e30cf92cc1" style="font-size: 1rem;"><img src="https://lh5.googleusercontent.com/qE_PaXNcEbECok0Xfbj89ubXSw3h-Yt3l_HcM3Xai_QlQcLo9suGkEIX_x1bONqRLotS7QFRogRdEytPiqBHcATwjpiUBUaFLzs5GzxTW1zNWjeZe0gFyrvejnNMmJI5MNaEk0Bnmp8" alt="angle" width="500" height="524" class="img-responsive atto_image_button_text-bottom"></b></p>
<p
style="text-align: left;"><span style="font-size: 1rem;"></span></p>
<ul style="">
<li dir="ltr" style="font-weight: bold;">
<p dir="ltr" role="presentation" style=""><span style="font-weight: normal;">\(r_S\) = the vector from the center of the earth to the satellite</span></p>
</li>
<li dir="ltr" style="">
<p dir="ltr" role="presentation">\(r_e\) = the vector from the center of the earth to the earth station</p>
</li>
<li dir="ltr" style="">
<p dir="ltr" role="presentation">d = the vector from the earth station to the satellite</p>
</li>
<li dir="ltr" style="">
<p dir="ltr" role="presentation">These vectors are in the same plane and from a triangle</p>
</li>
<li dir="ltr" style="">
<p dir="ltr" role="presentation">\(\gamma\) = angle measured between re and \(r_S\) , i.e. the angle between the earth station and the satellite.</p>
</li>
<li dir="ltr" style="">
<p dir="ltr" role="presentation" style="">\(\psi\) = angle measured from \(r_e\) to d</p>
</li>
</ul><span id="docs-internal-guid-da2fbfc2-7fff-6714-037c-8f92356d7f04"><ul style=""><li dir="ltr" style=""><p dir="ltr" role="presentation" style="">\(\gamma\) can be calculated from the following equation:<br><br><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>cos</mi><mo>(</mo><mi>γ</mi><mo>)</mo><mo>=</mo><mi>cos</mi><mo>(</mo><msub><mi>L</mi><mi>e</mi></msub><mo>)</mo><mi>cos</mi><mo>(</mo><msub><mi>L</mi><mi>S</mi></msub><mo>)</mo><mi>cos</mi><mo>(</mo><msub><mi>l</mi><mi>S</mi></msub><mo>-</mo><msub><mi>l</mi><mi>e</mi></msub><mo>)</mo><mo>+</mo><mi>sin</mi><mo>(</mo><msub><mi>L</mi><mi>e</mi></msub><mo>)</mo><mi>sin</mi><mo>(</mo><msub><mi>L</mi><mi>S</mi></msub><mo>)</mo><annotation encoding="LaTeX">$$\cos (\gamma ) = \cos (L_e)\cos (L_S)\cos (l_S-l_e)+\sin (L_e)\sin(L_S)$$</annotation></semantics></math></p></li></ul><p dir="ltr" style="">Where:</p><ul style=""><ul style=""><li dir="ltr" style=""><p dir="ltr" role="presentation">\(L_e\) = related to the earth station north Latitude (earth station is north of equator)</p></li><li dir="ltr" style=""><p dir="ltr" role="presentation">\(L_S\) = Subsatellite point at north Latitude</p></li><li dir="ltr" style=""><p dir="ltr" role="presentation">\(l_e\) = number in degree in longitude that earth station is west from the Greenwich meridian</p></li><li dir="ltr" style=""><p dir="ltr" role="presentation" style="">\(l_S\) = west longitude</p></li></ul></ul><span id="docs-internal-guid-c877d197-7fff-28c1-d222-3a1f1e55fc7b"><ul style=""><li dir="ltr" style=""><p dir="ltr" role="presentation" style="">The law of cosines allow us to relate the magnitudes of the vectors joining the center of the earth, the satellite, and the earth station. Therefore, the distance between earth station and satellite:</p></li></ul></span>
<math
xmlns="http://www.w3.org/1998/Math/MathML">
<semantics>
<annotation encoding="LaTeX">\(d = r_S \left[1+\left(\frac{r_e}{r_s}\right)^2-2\left(\frac{r_e}{r_s}\right)\cos(\gamma)\right]^\frac{1}{2}\)</annotation>
</semantics>
</math><br></span><br>
<p></p>
<p style=""><span style=""></span></p>
<p dir="ltr" style="">Since the local and horizontal plane at the earth station is perpendicular to the \(r_e\). The elevation angle, El, is related to the central angle \(\psi\) by:</p><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>E</mi><mi>l</mi><mo>=</mo><mi>Ψ</mi><mo>-</mo><mn>90</mn><mo>°</mo><annotation encoding="LaTeX">$$El= \Psi- 90^{\circ}$$</annotation></semantics></math>
<p></p>
<p style=""><span style=""></span></p>
<p dir="ltr">From the law of sines:</p><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mfrac><msub><mi>r</mi><mi>s</mi></msub><mrow><mi>sin</mi><mo>(</mo><mi>Ψ</mi><mo>)</mo></mrow></mfrac><mo>=</mo><mfrac><mi>d</mi><mrow><mi>sin</mi><mo>(</mo><mi>γ</mi><mo>)</mo></mrow></mfrac><annotation encoding="LaTeX">$$\frac{r_s}{\sin(\Psi)}=\frac{d}{\sin(\gamma)}$$</annotation></semantics></math>
<p></p>
<p style=""><span style=""><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>cos</mi><mo>(</mo><mi>Ψ</mi><mo>-</mo><mn>90</mn><mo>°</mo><mo>)</mo><mo>=</mo><mi>sin</mi><mo>(</mo><mi>Ψ</mi><mo>)</mo><mo>=</mo><mi>cos</mi><mrow><mi>E</mi><mi>l</mi></mrow><annotation encoding="LaTeX">$$\cos(\Psi-90^{\circ}) = \sin(\Psi)=\cos{El}$$</annotation></semantics></math></span></p>
<p
style=""><span style=""></span></p>
<p dir="ltr">Combining the above three equations:</p>
<p dir="ltr"></p><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>cos</mi><mo>(</mo><mi>E</mi><mi>l</mi><mo>)</mo><mo>=</mo><msub><mi>r</mi><mi>s</mi></msub><mo>×</mo><mfrac><mrow><mi>sin</mi><mo>(</mo><mi>γ</mi><mo>)</mo></mrow><mi>d</mi></mfrac><annotation encoding="LaTeX">$$\cos(El) = r_s \times \frac{\sin(\gamma)}{d} $$</annotation></semantics></math><br><span><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo>=</mo><mfrac><mrow><mi>sin</mi><mo>(</mo><mi>γ</mi><mo>)</mo></mrow><msup><mfenced close="]" open="["><mrow><mn>1</mn><mo>+</mo><msup><mfenced><mfrac><msub><mi>r</mi><mi>e</mi></msub><msub><mi>e</mi><mi>s</mi></msub></mfrac></mfenced><mn>2</mn></msup><mo>-</mo><mn>2</mn><mfenced><mfrac><msub><mi>r</mi><mi>e</mi></msub><msub><mi>r</mi><mi>s</mi></msub></mfrac></mfenced><mi>cos</mi><mo>(</mo><mi>γ</mi><mo>)</mo></mrow></mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></msup></mfrac><annotation encoding="LaTeX">$$\quad \quad~~~=\frac{\sin(\gamma)}{\left[1+\left(\frac{r_e}{e_s}\right)^2 -2\left(\frac{r_e}{r_s}\right)\cos(\gamma)\right]^\frac{1}{2}}$$</annotation></semantics></math></span><br><br>
<span
id="docs-internal-guid-13cec965-7fff-31c9-595f-a0530817198a">
<h3><span><span><b>Elevation Angle Calculation of GEO Satellite</b></span></span>
</h3>
<p><span><span></span></span>
</p>
<p dir="ltr">For Geostationary Satellite:</p>
<ul>
<li dir="ltr">
<p dir="ltr" role="presentation">Subsatellite point is on the equator at longitude \(l_S\) and the Latitude \(L_S\) is 0.</p>
</li>
<li dir="ltr">
<p dir="ltr" role="presentation">Geosynchronous radius \(r_S \)= 42,164.17 Km</p>
</li>
<li dir="ltr">
<p dir="ltr" role="presentation">Since \(L_S\) = 0,<br><br><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>cos</mi><mo>(</mo><mi>γ</mi><mo>)</mo><mo>=</mo><mi>c</mi><mi>o</mi><mi>s</mi><mo>(</mo><msub><mi>L</mi><mi>e</mi></msub><mo>)</mo><mo>×</mo><mi>cos</mi><mo>(</mo><msub><mi>l</mi><mi>s</mi></msub><mo>-</mo><msub><mi>l</mi><mi>e</mi></msub><mo>)</mo><annotation encoding="LaTeX">$$\cos (\gamma) = cos (L_e) \times \cos (l_s-l_e)$$</annotation></semantics></math></p>
</li>
<li dir="ltr">
<p dir="ltr" role="presentation">Since \(r_S\)=42,164.17 Km and \(r_e\) = 6378.17 Km, hence <br><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>d</mi><mo>=</mo><mn>42</mn><mo>,</mo><mn>164</mn><mo>.</mo><mn>17</mn><msup><mfenced close="]" open="["><mrow><mn>1</mn><mo>.</mo><mn>02288235</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>30253825</mn><mo>×</mo><mi>cos</mi><mo>(</mo><mi>γ</mi><mo>)</mo></mrow></mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></msup><annotation encoding="LaTeX">$$d= 42,164.17 \left[1.02288235 - 0.30253825 \times \cos (\gamma)\right]^\frac{1}{2}$$</annotation></semantics></math><br>
<math
xmlns="http://www.w3.org/1998/Math/MathML">
<semantics>
<mi>cos</mi>
<mo>(</mo>
<mi>E</mi>
<mi>l</mi>
<mo>)</mo>
<mo>=</mo>
<mfrac>
<mrow>
<mi>sin</mi>
<mo>(</mo>
<mi>γ</mi>
<mo>)</mo>
</mrow>
<msup>
<mfenced close="]" open="[">
<mrow>
<mn>1</mn>
<mo>.</mo>
<mn>02288235</mn>
<mo>-</mo>
<mn>0</mn>
<mo>.</mo>
<mn>32053825</mn>
<mi>cos</mi>
<mo>(</mo>
<mi>γ</mi>
<mo>)</mo>
</mrow>
</mfenced>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</msup>
</mfrac>
<annotation encoding="LaTeX">$$\cos(El) = \frac{\sin (\gamma)}{\left[1.02288235 -0.32053825\cos(\gamma)\right]^\frac{1}{2}}$$</annotation>
</semantics>
</math>
</p>
</li>
</ul><b><b><br></b></b>
</span><br><br>
<p></p>
Как показано на следующем рисунке, в выводе отображаются лишние буквы и повторяющиеся уравнения! Я попытался создать другую страницу, и результат был таким же. Любая помощь приветствуется заранее.