Motion Switching and Chaos of a Particle in a Generalized Fermi-Acceleration Oscillator

<table>Relative domains and boundaries definition: (a) <svg height="14.57625" id="M73" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 33.763748 14.57625" width="33.763748" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.57625)">
<text transform="matrix(1,0,0,-1,0.498,2.711)">
<tspan style="font-size: 12.50px; " x="0" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="4.1635389" y="0">𝑧</tspan>
<tspan style="font-size: 12.50px; " x="10.402596" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="22.230547" y="0">̇</tspan>
<tspan style="font-size: 12.50px; " x="15.616397" y="0">𝑧</tspan>
<tspan style="font-size: 12.50px; " x="21.855453" y="0">)</tspan>
</text>
</g>
</svg>-plane for particle, (b) <svg height="14.57625" id="M74" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 33.763748 14.57625" width="33.763748" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.57625)">
<text transform="matrix(1,0,0,-1,0.498,2.711)">
<tspan style="font-size: 12.50px; " x="0" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="10.790193" y="0">̇</tspan>
<tspan style="font-size: 12.50px; " x="4.1635389" y="0">𝑧</tspan>
<tspan style="font-size: 12.50px; " x="10.402596" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="22.230547" y="0">̈</tspan>
<tspan style="font-size: 12.50px; " x="15.616397" y="0">𝑧</tspan>
<tspan style="font-size: 12.50px; " x="21.855453" y="0">)</tspan>
</text>
</g>
</svg>-plane for particle, (c) <svg height="14.57625" id="M75" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 33.763748 14.57625" width="33.763748" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.57625)">
<text transform="matrix(1,0,0,-1,0.498,2.711)">
<tspan style="font-size: 12.50px; " x="0" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="4.1635389" y="0">𝑧</tspan>
<tspan style="font-size: 12.50px; " x="10.402596" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="22.230547" y="0">̇</tspan>
<tspan style="font-size: 12.50px; " x="15.616397" y="0">𝑧</tspan>
<tspan style="font-size: 12.50px; " x="21.855453" y="0">)</tspan>
</text>
</g>
</svg>-plane for piston, (d) <svg height="14.57625" id="M76" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 33.763748 14.57625" width="33.763748" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.57625)">
<text transform="matrix(1,0,0,-1,0.498,2.711)">
<tspan style="font-size: 12.50px; " x="0" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="10.790193" y="0">̇</tspan>
<tspan style="font-size: 12.50px; " x="4.1635389" y="0">𝑧</tspan>
<tspan style="font-size: 12.50px; " x="10.402596" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="22.230547" y="0">̈</tspan>
<tspan style="font-size: 12.50px; " x="15.616397" y="0">𝑧</tspan>
<tspan style="font-size: 12.50px; " x="21.855453" y="0">)</tspan>
</text>
</g>
</svg>-plane for piston.</table>

Mathematical Problems in Engineering

fig4

Figure 4

Figure 4: Motion Switching and Chaos of a Particle in a Generalized Fermi-Acceleration Oscillator 