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

Figure 19

Phase planes. Solid and dashed curves represent motions of particle and piston, respectively, (𝑚₁=0.01, 𝑚₂=1, 𝑘=10, 𝑐=6, 𝑒₁=0.9, 𝑄=0.5): (a) 𝑃₀₃₂ (Ω=6.5, 𝑒₂=0.01) (𝑡₀=0.70442282, 𝑥⁽¹⁾₀=𝑥⁽²⁾₀=−0.38755043, 𝑥̇⁽¹⁾₀=1.90527812, 𝑥̇⁽²⁾₀=1.96895970), (b) 𝑃₃₂ (Ω=11.8, 𝑒₂=0.01) (𝑡₀=0.51035890, 𝑥⁽¹⁾₀=𝑥⁽²⁾₀=0.01422235, 𝑥̇⁽¹⁾₀=0.87719897, 𝑥̇⁽²⁾₀=2.83304464), (c) 𝑃₍₂₁₃₎ (Ω=6.7, 𝑒₂=0.7) (𝑡₀=0.07416331, 𝑥⁽¹⁾₀=1.0, 𝑥̇⁽¹⁾₀=5.41048884, 𝑥⁽²⁾₀=0.32803506, 𝑥̇⁽²⁾₀=1.15044594), (d) 𝑃₍₂₁₃₎₂ (Ω=6.5, 𝑒₂=0.7) (𝑡₀=0.08347153, 𝑥⁽¹⁾₀=1.0, 𝑥̇⁽¹⁾₀=5.54878710, 𝑥⁽²⁾₀=0.34730036, 𝑥̇⁽²⁾₀=0.98801503), (e) 𝑃₁₂ (Ω=22.7, 𝑒₂=0.7) (𝑡₀=0.08699328, 𝑥⁽¹⁾₀=1.0, 𝑥̇⁽¹⁾₀=8.11298196, 𝑥⁽²⁾₀=0.04059727, 𝑥̇⁽²⁾₀=−1.64929089), and (f) 𝑃₍₁₂₎₂ (Ω=20.4, 𝑒₂=0.7) (𝑡₀=0.39975776, 𝑥⁽¹⁾₀=1.0, 𝑥̇⁽¹⁾₀=8.17571963, 𝑥⁽²⁾₀=0.07102098, 𝑥̇⁽²⁾₀=−1.44790328).

(a)

(b)

(c)

(d)

(e)

(f)