Numerical Validation of the Delaunay Normalization and the Krylov-Bogoliubov-Mitropolsky Method

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="927975.fig.006a" src="https://static.hindawi.com/articles/mpe/volume-2014/927975/figures/927975.fig.006a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b>Semimajor axis errors</td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="927975.fig.006b" src="https://static.hindawi.com/articles/mpe/volume-2014/927975/figures/927975.fig.006b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b>Eccentricity errors</td></tr></table></td></tr><tr class="fig-image" id="c"><td><img alt="927975.fig.006c" src="https://static.hindawi.com/articles/mpe/volume-2014/927975/figures/927975.fig.006c.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(c) </b>Inclination errors</td></tr></table></td></tr><tr class="fig-image" id="d"><td><img alt="927975.fig.006d" src="https://static.hindawi.com/articles/mpe/volume-2014/927975/figures/927975.fig.006d.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(d) </b>Argument of the perigee errors</td></tr></table></td></tr></table>

<table>Box and whisker plots for DN and KBM orbital element errors with <svg height="11.125" id="M130" style="vertical-align:-0.30096pt" version="1.1" viewbox="0 0 54.9375 11.125" width="54.9375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.862)"><path d="M391 364q0 -28 -20.5 -53.5t-50 -43.5t-70 -34t-73.5 -25t-68 -17v-29q0 -48 20 -81t65 -33q73 0 157 76l16 -23q-107 -113 -221 -113q-21 0 -40.5 6.5t-39 22t-31.5 47t-12 75.5q0 69 33.5 139.5t95.5 114.5q77 55 143 55q42 0 69 -24.5t27 -59.5zM313 350
q0 26 -14.5 40.5t-37.5 14.5q-32 0 -44 -7q-82 -46 -104 -175q200 49 200 127z" id="x1D452"></path></g><g transform="matrix(.017,-0,0,-.017,11.809,10.862)"><path d="M512 -3l-437 233v51l437 233v-58l-378 -200v-2l378 -199v-58z" id="x3C"></path></g><g transform="matrix(.017,-0,0,-.017,26.513,10.862)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g><g transform="matrix(.017,-0,0,-.017,34.672,10.862)"><path d="M113 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5t16 -40.5q0 -26 -16 -42t-41 -16z" id="x2E"></path></g><g transform="matrix(.017,-0,0,-.017,38.548,10.862)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g><g transform="matrix(.017,-0,0,-.017,46.707,10.862)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g>
</svg> for a time span of 7 days.</table>

Mathematical Problems in Engineering

fig6

Figure 6

Figure 6: Numerical Validation of the Delaunay Normalization and the Krylov-Bogoliubov-Mitropolsky Method 