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洛伦兹-84吸引子

洛伦兹-84吸引子
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2017-08-30 19:11
向量函数微积分参数方程几何作图
所属专题 UQ-Applied Mathematical Analysis
①本范例演示了洛伦兹-84吸引子的三维动态轨迹，展示了混沌系统的复杂运动模式；②涉及的核心数学概念包括微分方程、参数方程、三维空间可视化；③作图要点提炼自构造摘要，使用了对象如按钮(button1, button2等)、滑块(strength, n等)、变量(t, A, k1, j1等)以及函数定义(f, g, F, G, H)；④适合高中及以上数学、物理学生及对混沌理论感兴趣的爱好者，用于教学演示和探索参数对系统行为的影响。

GeoGebra 命令及参数

  1. Numeric strength(2)
  2. Numeric n(12)
  3. Numeric h(0.005)
  4. Numeric speed(1)
  5. Numeric t(1.1)
  6. Numeric b(4)
  7. x(CornerThreeD[-1, 3])
  8. x(CornerThreeD[-1, 1])
  9. y(CornerThreeD[-1, 3])
  10. y(CornerThreeD[-1, 1])
  11. z(CornerThreeD[-1, 5])
  12. z(CornerThreeD[-1, 3])
  13. {(1.698887608931714, 2.0504010462068276, 0.5760998599060181), (-0.32313175376458236, -2.9202990154971715, -0.18578885707181514), (-0.703865778294956, -1.9430964880606907, -0.6836063941861303), (-1.380
  14. {0.17970358504534012, 1.0858554568201608, 1.8656741461820978, -2.105328338669458, -0.09429440885513785, 1.1553698756657758, -3.8389210160410334, -0.6083397544876137, 0.7633749698157235, 0.740578123608
  15. {-15.374318016002096, 13.888842084295998, 14.593751230568177, -3.956097146486112, -12.745440615259469, 4.042605164879367, -6.132644574233076, -6.935372589792351, -0.8253948753445224, -3.25692887787045
  16. {7.046504078530084, -9.860146301731675, 5.395055257497853, 20.34802139700003, 11.332781222476173, 14.719495976770112, 6.647815896271328, 16.05799165648909, -0.13194602490549057, -0.304139995327789, 26
  17. {0.14263420190131537, 1.073177675798263, 1.8403453563275223, -2.171186219318251, -0.13727512694310473, 1.1145728801495793, -3.8385632775683156, -0.6590283959830945, 0.7706154521125699, 0.7497481302166
  18. {-15.726236659530038, 14.353924922114915, 14.448768875013045, -4.616472714708148, -13.21199693493403, 3.5084403417098216, -6.13440647299943, -7.485936756429744, -0.8324320543325774, -3.263152289459468
  19. {6.482256590243258, -9.381851393274065, 6.2411372386916195, 20.212863071054336, 10.911175078624257, 14.961235724562984, 6.4222146369011845, 15.86450484742283, -0.1182903059856168, -0.3302432585945161,
  20. {0.1502311220547381, 1.0795865572520538, 1.845259545686293, -2.1603127872217405, -0.12966825270830995, 1.1198349047290317, -3.835477678314005, -0.6512566394969888, 0.7705397797892708, 0.75006368309443
  21. {-15.70507786014791, 14.337310623421345, 14.401281785974415, -4.613770116461824, -13.197670537907337, 3.4966889075101313, -6.131417587875186, -7.480774067436194, -0.8325618877186312, -3.26307527780630
  22. {6.465423640740355, -9.361284829889847, 6.240397848061697, 20.188910928780572, 10.891556635928817, 14.94125097106652, 6.422583295873837, 15.844231563426336, -0.11821747880329625, -0.33015616596802744,
  23. {0.1138063390998365, 1.0661571733780622, 1.8190163531705332, -2.2258139322216843, -0.17212378235391235, 1.0786380161723486, -3.834105788804237, -0.7016486354797227, 0.7776879484214403, 0.7592771377217
  24. {-16.034813147968713, 14.785603337838339, 14.207710131870245, -5.265389160877023, -13.648449476125858, 2.9506561786623635, -6.127283968118942, -8.023809956148822, -0.8397332219654894, -3.2692749213130
  25. {5.885793998503074, -8.862409810988387, 7.083563768640467, 20.030457222642156, 10.451626583236497, 15.162952864578756, 6.199377096016536, 15.631318733389202, -0.10456024123868085, -0.35641582464420085
  26. Numeric a(0.25)
  27. Numeric f(8)
  28. Numeric g(1)
  29. F(x, y, z) = (strength * (((-a) * x) - (y * y) - (z * z) + (a * f)))
  30. G(x, y, z) = (strength * ((-y) + (x * y) - ((b * x) * z) + g))
  31. H(x, y, z) = (strength * ((-z) + ((b * x) * y) + (x * z)))

AI 绘图提示语参考

绘制一个三维动态轨迹图，展示洛伦兹-84吸引子的复杂运动模式，该轨迹由三个微分方程定义的参数方程生成，方程涉及变量x、y、z和参数strength、n、h等，轨迹在三维空间中呈现混沌系统的运动特征，背景为三维坐标系。
以上提示语为根据原始绘图命令整理而来，仅供参考。