Modified Chebyshev-Picard Iteration Methods for Station-Keeping of Translunar Halo Orbits

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr class="thead"><td align="left"> Variable</td><td align="center"> Nondimensional value</td></tr><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr><td align="left"><span style="width: 33.525002px;"><svg height="16.4125" id="M85" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 33.525002 16.4125" width="33.525002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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q0 16 13.5 31.5t28.5 15.5q12 0 17 -11q5 -10 25 -10q22 0 57.5 36t89.5 111l-40 108q-22 58 -36 58q-21 0 -67 -57l-19 20q81 107 125 107q17 0 30 -22t39 -88l22 -55q68 92 108.5 128.5t74.5 36.5q20 0 32.5 -14t12.5 -30z" id="x1D465"></path></g><g transform="matrix(.017,-0,0,-.017,9.565,12.138)"><path d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" id="x28"></path></g><g transform="matrix(.017,-0,0,-.017,15.446,12.138)"><use xlink:href="#x1D461"></use></g>
<g transform="matrix(.012,-0,0,-.012,21.238,16.212)"><use xlink:href="#x30"></use></g>
<g transform="matrix(.017,-0,0,-.017,27.575,12.138)"><path d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" id="x29"></path></g>
</svg></span></td><td align="center"> −0.390895010335809</td></tr><tr><td align="left"><span style="width: 32.487499px;"><svg height="16.4125" id="M86" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 32.487499 16.4125" width="32.487499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.138)"><path d="M475 445l-64 -69q-119 -128 -289 -280q27 6 81 -15q66 -26 102 -26q48 0 111 93l23 -19q-41 -84 -75.5 -116.5t-73.5 -32.5q-37 0 -147 53q-43 21 -63 7q-22 -15 -38 -41q-4 -7 -11 -7q-8 10 -8 26q0 38 47 83l292 273q-32 -5 -67 -1q-63 7 -105 7q-32 0 -53.5 -22
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<g transform="matrix(.012,-0,0,-.012,20.2,16.212)"><use xlink:href="#x30"></use></g>
<g transform="matrix(.017,-0,0,-.017,26.537,12.138)"><use xlink:href="#x29"></use></g>
</svg></span></td><td align="center"> 0.353556629315019</td></tr><tr><td align="left"><span style="width: 39.6875px;"><svg height="19.375" id="M87" style="vertical-align:-5.76984pt" version="1.1" viewbox="0 0 39.6875 19.375" width="39.6875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.017,-0,0,-.017,33.75,12.138)"><use xlink:href="#x29"></use></g>
</svg></span></td><td align="center"> 1.554577497503360</td></tr><tr><td align="left"><span style="width: 19.125px;"><svg height="18.75" id="M88" style="vertical-align:-5.73163pt" version="1.1" viewbox="0 0 19.125 18.75" width="19.125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg></span></td><td align="center">3.336429964438981</td></tr><tr class="table-tr"><td colspan="2"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Mathematical Problems in Engineering

tab2

Table 2

Table 2: Modified Chebyshev-Picard Iteration Methods for Station-Keeping of Translunar Halo Orbits 