Моделирование эффекта Джанибекова
В данном примере будет показано моделирование эффекта Джанибекова - нестабильного вращения твердого тела вокруг средней оси инерции. Модель демонстрирует, как небольшое возмущение при вращении вокруг промежуточной оси приводит к периодическому "перевороту" объекта в пространстве.
Эффект Джанибекова проявляется при вращении асимметричного твердого тела вокруг оси с промежуточным моментом инерции. Согласно теореме о промежуточной оси, такое вращение неустойчиво - малейшее возмущение приводит к периодическому "перевороту" объекта.
Условие возникновения: I₁ < I₂ < I₃, где I₂ - момент инерции относительно средней оси.
Для реализации модели вращения в данном примере используется блок Engee Function, в котором, с помощью кода, были реализованы уравнения Эйлера для свободного вращения:
Также в этом блоке описывается кинематика кватернионов:
На вход блока подаются состояния интегралы от производных кватернионов и угловых скоростей, рассчитываемые в блоке Интегрирование, имеющим следующее устройство:
С помощью блоков шин сигналы компонуются для дальнейшего использования. Из Шины 3 сигнал идёт в блок, в котором шина преобразуется в вектор и, затем, подаётся на вход блока Преобразования кватерниона в матрицу поворота.
Определение функции для загрузки и запуска модели:
Out[0]:
start_model_engee (generic function with 1 method)
Вывод данных в отдельную переменную:
Вывод данных в отдельные переменные для их анализа и построения визуализации:
Определение функции для создания Т-образной геометрической фигуры:
Out[0]:
create_t_figure (generic function with 1 method)
Определение функции для создания анимации движения тела:
Out[0]:
create_djanibekov_animation_plots (generic function with 1 method)
Создание анимации движения тела и её визуализация:
Анимация сохранена в файл: djanibekov_effect_plots.gif
[ Info: Saved animation to /user/djanibekov_effect_plots.gif
Переворот можно отследить на графике по смене знака угловой скорости вокруг оси Y, это происходит каждые 4 секунды.
В данном примере была продемонстрирована модель эффекта Джанибекова. Модель можно модифицировать и использовать в различных областях для задач наведения, слежения за целями и для управления ориентацией манипуляторов.
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3.161, 3.162, 3.163, 3.164, 3.165, 3.166, 3.167, 3.168, 3.169, 3.17, 3.171, 3.172, 3.173, 3.174, 3.175, 3.176, 3.177, 3.178, 3.179, 3.18, 3.181, 3.182, 3.183, 3.184, 3.185, 3.186, 3.187, 3.188, 3.189, 3.19, 3.191, 3.192, 3.193, 3.194, 3.195, 3.196, 3.197, 3.198, 3.199, 3.2, 3.201, 3.202, 3.203, 3.204, 3.205, 3.206, 3.207, 3.208, 3.209, 3.21, 3.211, 3.212, 3.213, 3.214, 3.215, 3.216, 3.217, 3.218, 3.219, 3.22, 3.221, 3.222, 3.223, 3.224, 3.225, 3.226, 3.227, 3.228, 3.229, 3.23, 3.231, 3.232, 3.233, 3.234, 3.235, 3.236, 3.237, 3.238, 3.239, 3.24, 3.241, 3.242, 3.243, 3.244, 3.245, 3.246, 3.247, 3.248, 3.249, 3.25, 3.251, 3.252, 3.253, 3.254, 3.255, 3.256, 3.257, 3.258, 3.259, 3.26, 3.261, 3.262, 3.263, 3.264, 3.265, 3.266, 3.267, 3.268, 3.269, 3.27, 3.271, 3.272, 3.273, 3.274, 3.275, 3.276, 3.277, 3.278, 3.279, 3.28, 3.281, 3.282, 3.283, 3.284, 3.285, 3.286, 3.287, 3.288, 3.289, 3.29, 3.291, 3.292, 3.293, 3.294, 3.295, 3.296, 3.297, 3.298, 3.299, 3.3, 3.301, 3.302, 3.303, 3.304, 3.305, 3.306, 3.307, 3.308, 3.309, 3.31, 3.311, 3.312, 3.313, 3.314, 3.315, 3.316, 3.317, 3.318, 3.319, 3.32, 3.321, 3.322, 3.323, 3.324, 3.325, 3.326, 3.327, 3.328, 3.329, 3.33, 3.331, 3.332, 3.333, 3.334, 3.335, 3.336, 3.337, 3.338, 3.339, 3.34, 3.341, 3.342, 3.343, 3.344, 3.345, 3.346, 3.347, 3.348, 3.349, 3.35, 3.351, 3.352, 3.353, 3.354, 3.355, 3.356, 3.357, 3.358, 3.359, 3.36, 3.361, 3.362, 3.363, 3.364, 3.365, 3.366, 3.367, 3.368, 3.369, 3.37, 3.371, 3.372, 3.373, 3.374, 3.375, 3.376, 3.377, 3.378, 3.379, 3.38, 3.381, 3.382, 3.383, 3.384, 3.385, 3.386, 3.387, 3.388, 3.389, 3.39, 3.391, 3.392, 3.393, 3.394, 3.395, 3.396, 3.397, 3.398, 3.399, 3.4, 3.401, 3.402, 3.403, 3.404, 3.405, 3.406, 3.407, 3.408, 3.409, 3.41, 3.411, 3.412, 3.413, 3.414, 3.415, 3.416, 3.417, 3.418, 3.419, 3.42, 3.421, 3.422, 3.423, 3.424, 3.425, 3.426, 3.427, 3.428, 3.429, 3.43, 3.431, 3.432, 3.433, 3.434, 3.435, 3.436, 3.437, 3.438, 3.439, 3.44, 3.441, 3.442, 3.443, 3.444, 3.445, 3.446, 3.447, 3.448, 3.449, 3.45, 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3.886, 3.887, 3.888, 3.889, 3.89, 3.891, 3.892, 3.893, 3.894, 3.895, 3.896, 3.897, 3.898, 3.899, 3.9, 3.901, 3.902, 3.903, 3.904, 3.905, 3.906, 3.907, 3.908, 3.909, 3.91, 3.911, 3.912, 3.913, 3.914, 3.915, 3.916, 3.917, 3.918, 3.919, 3.92, 3.921, 3.922, 3.923, 3.924, 3.925, 3.926, 3.927, 3.928, 3.929, 3.93, 3.931, 3.932, 3.933, 3.934, 3.935, 3.936, 3.937, 3.938, 3.939, 3.94, 3.941, 3.942, 3.943, 3.944, 3.945, 3.946, 3.947, 3.948, 3.949, 3.95, 3.951, 3.952, 3.953, 3.954, 3.955, 3.956, 3.957, 3.958, 3.959, 3.96, 3.961, 3.962, 3.963, 3.964, 3.965, 3.966, 3.967, 3.968, 3.969, 3.97, 3.971, 3.972, 3.973, 3.974, 3.975, 3.976, 3.977, 3.978, 3.979, 3.98, 3.981, 3.982, 3.983, 3.984, 3.985, 3.986, 3.987, 3.988, 3.989, 3.99, 3.991, 3.992, 3.993, 3.994, 3.995, 3.996, 3.997, 3.998, 3.999, 4, 4.001, 4.002, 4.003, 4.004, 4.005, 4.006, 4.007, 4.008, 4.009, 4.01, 4.011, 4.012, 4.013, 4.014, 4.015, 4.016, 4.017, 4.018, 4.019, 4.02, 4.021, 4.022, 4.023, 4.024, 4.025, 4.026, 4.027, 4.028, 4.029, 4.03, 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4.176, 4.177, 4.178, 4.179, 4.18, 4.181, 4.182, 4.183, 4.184, 4.185, 4.186, 4.187, 4.188, 4.189, 4.19, 4.191, 4.192, 4.193, 4.194, 4.195, 4.196, 4.197, 4.198, 4.199, 4.2, 4.201, 4.202, 4.203, 4.204, 4.205, 4.206, 4.207, 4.208, 4.209, 4.21, 4.211, 4.212, 4.213, 4.214, 4.215, 4.216, 4.217, 4.218, 4.219, 4.22, 4.221, 4.222, 4.223, 4.224, 4.225, 4.226, 4.227, 4.228, 4.229, 4.23, 4.231, 4.232, 4.233, 4.234, 4.235, 4.236, 4.237, 4.238, 4.239, 4.24, 4.241, 4.242, 4.243, 4.244, 4.245, 4.246, 4.247, 4.248, 4.249, 4.25, 4.251, 4.252, 4.253, 4.254, 4.255, 4.256, 4.257, 4.258, 4.259, 4.26, 4.261, 4.262, 4.263, 4.264, 4.265, 4.266, 4.267, 4.268, 4.269, 4.27, 4.271, 4.272, 4.273, 4.274, 4.275, 4.276, 4.277, 4.278, 4.279, 4.28, 4.281, 4.282, 4.283, 4.284, 4.285, 4.286, 4.287, 4.288, 4.289, 4.29, 4.291, 4.292, 4.293, 4.294, 4.295, 4.296, 4.297, 4.298, 4.299, 4.3, 4.301, 4.302, 4.303, 4.304, 4.305, 4.306, 4.307, 4.308, 4.309, 4.31, 4.311, 4.312, 4.313, 4.314, 4.315, 4.316, 4.317, 4.318, 4.319, 4.32, 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3.288, 3.289, 3.29, 3.291, 3.292, 3.293, 3.294, 3.295, 3.296, 3.297, 3.298, 3.299, 3.3, 3.301, 3.302, 3.303, 3.304, 3.305, 3.306, 3.307, 3.308, 3.309, 3.31, 3.311, 3.312, 3.313, 3.314, 3.315, 3.316, 3.317, 3.318, 3.319, 3.32, 3.321, 3.322, 3.323, 3.324, 3.325, 3.326, 3.327, 3.328, 3.329, 3.33, 3.331, 3.332, 3.333, 3.334, 3.335, 3.336, 3.337, 3.338, 3.339, 3.34, 3.341, 3.342, 3.343, 3.344, 3.345, 3.346, 3.347, 3.348, 3.349, 3.35, 3.351, 3.352, 3.353, 3.354, 3.355, 3.356, 3.357, 3.358, 3.359, 3.36, 3.361, 3.362, 3.363, 3.364, 3.365, 3.366, 3.367, 3.368, 3.369, 3.37, 3.371, 3.372, 3.373, 3.374, 3.375, 3.376, 3.377, 3.378, 3.379, 3.38, 3.381, 3.382, 3.383, 3.384, 3.385, 3.386, 3.387, 3.388, 3.389, 3.39, 3.391, 3.392, 3.393, 3.394, 3.395, 3.396, 3.397, 3.398, 3.399, 3.4, 3.401, 3.402, 3.403, 3.404, 3.405, 3.406, 3.407, 3.408, 3.409, 3.41, 3.411, 3.412, 3.413, 3.414, 3.415, 3.416, 3.417, 3.418, 3.419, 3.42, 3.421, 3.422, 3.423, 3.424, 3.425, 3.426, 3.427, 3.428, 3.429, 3.43, 3.431, 3.432, 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3.578, 3.579, 3.58, 3.581, 3.582, 3.583, 3.584, 3.585, 3.586, 3.587, 3.588, 3.589, 3.59, 3.591, 3.592, 3.593, 3.594, 3.595, 3.596, 3.597, 3.598, 3.599, 3.6, 3.601, 3.602, 3.603, 3.604, 3.605, 3.606, 3.607, 3.608, 3.609, 3.61, 3.611, 3.612, 3.613, 3.614, 3.615, 3.616, 3.617, 3.618, 3.619, 3.62, 3.621, 3.622, 3.623, 3.624, 3.625, 3.626, 3.627, 3.628, 3.629, 3.63, 3.631, 3.632, 3.633, 3.634, 3.635, 3.636, 3.637, 3.638, 3.639, 3.64, 3.641, 3.642, 3.643, 3.644, 3.645, 3.646, 3.647, 3.648, 3.649, 3.65, 3.651, 3.652, 3.653, 3.654, 3.655, 3.656, 3.657, 3.658, 3.659, 3.66, 3.661, 3.662, 3.663, 3.664, 3.665, 3.666, 3.667, 3.668, 3.669, 3.67, 3.671, 3.672, 3.673, 3.674, 3.675, 3.676, 3.677, 3.678, 3.679, 3.68, 3.681, 3.682, 3.683, 3.684, 3.685, 3.686, 3.687, 3.688, 3.689, 3.69, 3.691, 3.692, 3.693, 3.694, 3.695, 3.696, 3.697, 3.698, 3.699, 3.7, 3.701, 3.702, 3.703, 3.704, 3.705, 3.706, 3.707, 3.708, 3.709, 3.71, 3.711, 3.712, 3.713, 3.714, 3.715, 3.716, 3.717, 3.718, 3.719, 3.72, 3.721, 3.722, 3.723, 3.724, 3.725, 3.726, 3.727, 3.728, 3.729, 3.73, 3.731, 3.732, 3.733, 3.734, 3.735, 3.736, 3.737, 3.738, 3.739, 3.74, 3.741, 3.742, 3.743, 3.744, 3.745, 3.746, 3.747, 3.748, 3.749, 3.75, 3.751, 3.752, 3.753, 3.754, 3.755, 3.756, 3.757, 3.758, 3.759, 3.76, 3.761, 3.762, 3.763, 3.764, 3.765, 3.766, 3.767, 3.768, 3.769, 3.77, 3.771, 3.772, 3.773, 3.774, 3.775, 3.776, 3.777, 3.778, 3.779, 3.78, 3.781, 3.782, 3.783, 3.784, 3.785, 3.786, 3.787, 3.788, 3.789, 3.79, 3.791, 3.792, 3.793, 3.794, 3.795, 3.796, 3.797, 3.798, 3.799, 3.8, 3.801, 3.802, 3.803, 3.804, 3.805, 3.806, 3.807, 3.808, 3.809, 3.81, 3.811, 3.812, 3.813, 3.814, 3.815, 3.816, 3.817, 3.818, 3.819, 3.82, 3.821, 3.822, 3.823, 3.824, 3.825, 3.826, 3.827, 3.828, 3.829, 3.83, 3.831, 3.832, 3.833, 3.834, 3.835, 3.836, 3.837, 3.838, 3.839, 3.84, 3.841, 3.842, 3.843, 3.844, 3.845, 3.846, 3.847, 3.848, 3.849, 3.85, 3.851, 3.852, 3.853, 3.854, 3.855, 3.856, 3.857, 3.858, 3.859, 3.86, 3.861, 3.862, 3.863, 3.864, 3.865, 3.866, 3.867, 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4.013, 4.014, 4.015, 4.016, 4.017, 4.018, 4.019, 4.02, 4.021, 4.022, 4.023, 4.024, 4.025, 4.026, 4.027, 4.028, 4.029, 4.03, 4.031, 4.032, 4.033, 4.034, 4.035, 4.036, 4.037, 4.038, 4.039, 4.04, 4.041, 4.042, 4.043, 4.044, 4.045, 4.046, 4.047, 4.048, 4.049, 4.05, 4.051, 4.052, 4.053, 4.054, 4.055, 4.056, 4.057, 4.058, 4.059, 4.06, 4.061, 4.062, 4.063, 4.064, 4.065, 4.066, 4.067, 4.068, 4.069, 4.07, 4.071, 4.072, 4.073, 4.074, 4.075, 4.076, 4.077, 4.078, 4.079, 4.08, 4.081, 4.082, 4.083, 4.084, 4.085, 4.086, 4.087, 4.088, 4.089, 4.09, 4.091, 4.092, 4.093, 4.094, 4.095, 4.096, 4.097, 4.098, 4.099, 4.1, 4.101, 4.102, 4.103, 4.104, 4.105, 4.106, 4.107, 4.108, 4.109, 4.11, 4.111, 4.112, 4.113, 4.114, 4.115, 4.116, 4.117, 4.118, 4.119, 4.12, 4.121, 4.122, 4.123, 4.124, 4.125, 4.126, 4.127, 4.128, 4.129, 4.13, 4.131, 4.132, 4.133, 4.134, 4.135, 4.136, 4.137, 4.138, 4.139, 4.14, 4.141, 4.142, 4.143, 4.144, 4.145, 4.146, 4.147, 4.148, 4.149, 4.15, 4.151, 4.152, 4.153, 4.154, 4.155, 4.156, 4.157, 4.158, 4.159, 4.16, 4.161, 4.162, 4.163, 4.164, 4.165, 4.166, 4.167, 4.168, 4.169, 4.17, 4.171, 4.172, 4.173, 4.174, 4.175, 4.176, 4.177, 4.178, 4.179, 4.18, 4.181, 4.182, 4.183, 4.184, 4.185, 4.186, 4.187, 4.188, 4.189, 4.19, 4.191, 4.192, 4.193, 4.194, 4.195, 4.196, 4.197, 4.198, 4.199, 4.2, 4.201, 4.202, 4.203, 4.204, 4.205, 4.206, 4.207, 4.208, 4.209, 4.21, 4.211, 4.212, 4.213, 4.214, 4.215, 4.216, 4.217, 4.218, 4.219, 4.22, 4.221, 4.222, 4.223, 4.224, 4.225, 4.226, 4.227, 4.228, 4.229, 4.23, 4.231, 4.232, 4.233, 4.234, 4.235, 4.236, 4.237, 4.238, 4.239, 4.24, 4.241, 4.242, 4.243, 4.244, 4.245, 4.246, 4.247, 4.248, 4.249, 4.25, 4.251, 4.252, 4.253, 4.254, 4.255, 4.256, 4.257, 4.258, 4.259, 4.26, 4.261, 4.262, 4.263, 4.264, 4.265, 4.266, 4.267, 4.268, 4.269, 4.27, 4.271, 4.272, 4.273, 4.274, 4.275, 4.276, 4.277, 4.278, 4.279, 4.28, 4.281, 4.282, 4.283, 4.284, 4.285, 4.286, 4.287, 4.288, 4.289, 4.29, 4.291, 4.292, 4.293, 4.294, 4.295, 4.296, 4.297, 4.298, 4.299, 4.3, 4.301, 4.302, 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