The Orbital Dynamics of Synchronous Satellites: Irregular Motions in the 2 : 1 Resonance

<table>Time behavior of <svg height="11.825" id="M250" style="vertical-align:-3.276pt" version="1.1" viewbox="0 0 15.9625 11.825" width="15.9625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path d="M536 404q0 -17 -13.5 -31.5t-26.5 -14.5q-8 0 -15 10q-11 14 -25 14q-22 0 -67 -50q-47 -52 -68 -82l37 -102q31 -88 55 -88t78 59l16 -23q-32 -48 -68.5 -78t-65.5 -30q-19 0 -37.5 20t-29.5 53l-41 116q-72 -106 -114.5 -147.5t-79.5 -41.5q-21 0 -34.5 14t-13.5 37
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(.012,-0,0,-.012,9.563,11.762)"><use xlink:href="#x34"></use></g>
</svg> angle for different values of <svg height="15.5375" id="M251" style="vertical-align:-3.276pt" version="1.1" viewbox="0 0 18.4375 15.5375" width="18.4375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.4)"><use xlink:href="#x1D436"></use></g>
<g transform="matrix(.012,-0,0,-.012,12.05,15.475)"><use xlink:href="#x31"></use></g>
</svg> given in Table <a href="../tab3/">3</a>.</table>

Mathematical Problems in Engineering

fig2

Figure 2

Figure 2: The Orbital Dynamics of Synchronous Satellites: Irregular Motions in the 2 : 1 Resonance 