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Прыгающий мячик (физическая модель)
Прыгающий мячик (физическая модель)
Автор
nkapyrinМоделирование отскока мяча в 1D решателе
Построим модель 1D динамики простой механической системы: модель взаимодействия материальной точки с поверхностью земли при падении под действием гравитации.
Описание и запуск модели
Представим себе самый простой сценарий для расчета динамики предмета, испытывающего взаимодействия с поверхностью.
Предмет — материальная точка, на которую действует гравитация, а при столкновении с поверхностью — импульс ускорения.
За взаимодействие с поверхностью отвечает блок Translational Hard Stop (Поступательные упоры). Один из полезных эффектов от использования 1D моделирования состоит в том, что мы без дополнительных усилий получаем немного более сложную модель реакции опоры, чем идеально упругий отскок.
Запустим модель и изучим результаты:
model = engee.open("physical_bouncing_ball.engee")
data = engee.run(model)
plot(
plot( data["x"].time, data["x"].value, c=1, label="Положение" ),
plot( data["dx"].time, data["dx"].value, c=2, label="Скорость" ),
plot( data["ddx"].time, data["ddx"].value, c=3, label="Ускорение" ),
layout=(3,1), lw=3
)
Модель собрана максимально просто, ничего не изменено в параметрах физического или глобального решателя, за исключением его перевода в режим "интегрирования по переменным шагам", Чтобы на графике были видны все импульсы ускорения.
Заключение
Такой подход — идеальный старт для моделирования вертикального движения. Когда нужно быстро проверить концепцию или понять базовую динамику системы, эти три блока дают готовое решение без лишней сложности.
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1.71, 1.711, 1.712, 1.713, 1.714, 1.715, 1.716, 1.717, 1.718, 1.719, 1.72, 1.721, 1.722, 1.723, 1.724, 1.725, 1.726, 1.727, 1.728, 1.729, 1.73, 1.731, 1.732, 1.733, 1.734, 1.735, 1.736, 1.737, 1.738, 1.739, 1.74, 1.741, 1.742, 1.743, 1.744, 1.745, 1.746, 1.747, 1.748, 1.749, 1.75, 1.751, 1.752, 1.753, 1.754, 1.755, 1.756, 1.757, 1.758, 1.759, 1.76, 1.761, 1.762, 1.763, 1.764, 1.765, 1.766, 1.767, 1.768, 1.769, 1.77, 1.771, 1.772, 1.773, 1.774, 1.775, 1.776, 1.777, 1.778, 1.779, 1.78, 1.781, 1.782, 1.783, 1.784, 1.785, 1.786, 1.787, 1.788, 1.789, 1.79, 1.791, 1.792, 1.793, 1.794, 1.795, 1.796, 1.797, 1.798, 1.799, 1.8, 1.801, 1.802, 1.803, 1.804, 1.805, 1.806, 1.807, 1.808, 1.809, 1.81, 1.811, 1.812, 1.813, 1.814, 1.815, 1.816, 1.817, 1.818, 1.819, 1.82, 1.821, 1.822, 1.823, 1.824, 1.825, 1.826, 1.827, 1.828, 1.829, 1.83, 1.831, 1.832, 1.833, 1.834, 1.835, 1.836, 1.837, 1.838, 1.839, 1.84, 1.841, 1.842, 1.843, 1.844, 1.845, 1.846, 1.847, 1.848, 1.849, 1.85, 1.851, 1.852, 1.853, 1.854, 1.855, 1.856, 1.857, 1.858, 1.859, 1.86, 1.861, 1.862, 1.863, 1.864, 1.865, 1.866, 1.867, 1.868, 1.869, 1.87, 1.871, 1.872, 1.873, 1.874, 1.875, 1.876, 1.877, 1.878, 1.879, 1.88, 1.881, 1.882, 1.883, 1.884, 1.885, 1.886, 1.887, 1.888, 1.889, 1.89, 1.891, 1.892, 1.893, 1.894, 1.895, 1.896, 1.897, 1.898, 1.899, 1.9, 1.901, 1.902, 1.903, 1.904, 1.905, 1.906, 1.907, 1.908, 1.909, 1.91, 1.911, 1.912, 1.913, 1.914, 1.915, 1.916, 1.917, 1.918, 1.919, 1.92, 1.921, 1.922, 1.923, 1.924, 1.925, 1.926, 1.927, 1.928, 1.929, 1.93, 1.931, 1.932, 1.933, 1.934, 1.935, 1.936, 1.937, 1.938, 1.939, 1.94, 1.941, 1.942, 1.943, 1.944, 1.945, 1.946, 1.947, 1.948, 1.949, 1.95, 1.951, 1.952, 1.953, 1.954, 1.955, 1.956, 1.957, 1.958, 1.959, 1.96, 1.961, 1.962, 1.963, 1.964, 1.965, 1.966, 1.967, 1.968, 1.969, 1.97, 1.971, 1.972, 1.973, 1.974, 1.975, 1.976, 1.977, 1.978, 1.979, 1.98, 1.981, 1.982, 1.983, 1.984, 1.985, 1.986, 1.987, 1.988, 1.989, 1.99, 1.991, 1.992, 1.993, 1.994, 1.995, 1.996, 1.997, 1.998, 1.999, 2, 2.001, 2.002, 2.003, 2.004, 2.005, 2.006, 2.007, 2.008, 2.009, 2.01, 2.011, 2.012, 2.013, 2.014, 2.015, 2.016, 2.017, 2.018, 2.019, 2.02, 2.021, 2.022, 2.023, 2.024, 2.025, 2.026, 2.027, 2.028, 2.029, 2.03, 2.031, 2.032, 2.033, 2.034, 2.035, 2.036, 2.037, 2.038, 2.039, 2.04, 2.041, 2.042, 2.043, 2.044, 2.045, 2.046, 2.047, 2.048, 2.049, 2.05, 2.051, 2.052, 2.053, 2.054, 2.055, 2.056, 2.057, 2.058, 2.059, 2.06, 2.061, 2.062, 2.063, 2.064, 2.065, 2.066, 2.067, 2.068, 2.069, 2.07, 2.071, 2.072, 2.073, 2.074, 2.075, 2.076, 2.077, 2.078, 2.079, 2.08, 2.081, 2.082, 2.083, 2.084, 2.085, 2.086, 2.087, 2.088, 2.089, 2.09, 2.091, 2.092, 2.093, 2.094, 2.095, 2.096, 2.097, 2.098, 2.099, 2.1, 2.101, 2.102, 2.103, 2.104, 2.105, 2.106, 2.107, 2.108, 2.109, 2.11, 2.111, 2.112, 2.113, 2.114, 2.115, 2.116, 2.117, 2.118, 2.119, 2.12, 2.121, 2.122, 2.123, 2.124, 2.125, 2.126, 2.127, 2.128, 2.129, 2.13, 2.131, 2.132, 2.133, 2.134, 2.135, 2.136, 2.137, 2.138, 2.139, 2.14, 2.141, 2.142, 2.143, 2.144, 2.145, 2.146, 2.147, 2.148, 2.149, 2.15, 2.151, 2.152, 2.153, 2.154, 2.155, 2.156, 2.157, 2.158, 2.159, 2.16, 2.161, 2.162, 2.163, 2.164, 2.165, 2.166, 2.167, 2.168, 2.169, 2.17, 2.171, 2.172, 2.173, 2.174, 2.175, 2.176, 2.177, 2.178, 2.179, 2.18, 2.181, 2.182, 2.183, 2.184, 2.185, 2.186, 2.187, 2.188, 2.189, 2.19, 2.191, 2.192, 2.193, 2.194, 2.195, 2.196, 2.197, 2.198, 2.199, 2.2, 2.201, 2.202, 2.203, 2.204, 2.205, 2.206, 2.207, 2.208, 2.209, 2.21, 2.211, 2.212, 2.213, 2.214, 2.215, 2.216, 2.217, 2.218, 2.219, 2.22, 2.221, 2.222, 2.223, 2.224, 2.225, 2.226, 2.227, 2.228, 2.229, 2.23, 2.231, 2.232, 2.233, 2.234, 2.235, 2.236, 2.237, 2.238, 2.239, 2.24, 2.241, 2.242, 2.243, 2.244, 2.245, 2.246, 2.247, 2.248, 2.249, 2.25, 2.251, 2.252, 2.253, 2.254, 2.255, 2.256, 2.257, 2.258, 2.259, 2.26, 2.261, 2.262, 2.263, 2.264, 2.265, 2.266, 2.267, 2.268, 2.269, 2.27, 2.271, 2.272, 2.273, 2.274, 2.275, 2.276, 2.277, 2.278, 2.279, 2.28, 2.281, 2.282, 2.283, 2.284, 2.285, 2.286, 2.287, 2.288, 2.289, 2.29, 2.291, 2.292, 2.293, 2.294, 2.295, 2.296, 2.297, 2.298, 2.299, 2.3, 2.301, 2.302, 2.303, 2.304, 2.305, 2.306, 2.307, 2.308, 2.309, 2.31, 2.311, 2.312, 2.313, 2.314, 2.315, 2.316, 2.317, 2.318, 2.319, 2.32, 2.321, 2.322, 2.323, 2.324, 2.325, 2.326, 2.327, 2.328, 2.329, 2.33, 2.331, 2.332, 2.333, 2.334, 2.335, 2.336, 2.337, 2.338, 2.339, 2.34, 2.341, 2.342, 2.343, 2.344, 2.345, 2.346, 2.347, 2.348, 2.349, 2.35, 2.351, 2.352, 2.353, 2.354, 2.355, 2.356, 2.357, 2.358, 2.359, 2.36, 2.361, 2.362, 2.363, 2.364, 2.365, 2.366, 2.367, 2.368, 2.369, 2.37, 2.371, 2.372, 2.373, 2.374, 2.375, 2.376, 2.377, 2.378, 2.379, 2.38, 2.381, 2.382, 2.383, 2.384, 2.385, 2.386, 2.387, 2.388, 2.389, 2.39, 2.391, 2.392, 2.393, 2.394, 2.395, 2.396, 2.397, 2.398, 2.399, 2.4, 2.401, 2.402, 2.403, 2.404, 2.405, 2.406, 2.407, 2.408, 2.409, 2.41, 2.411, 2.412, 2.413, 2.414, 2.415, 2.416, 2.417, 2.418, 2.419, 2.42, 2.421, 2.422, 2.423, 2.424, 2.425, 2.426, 2.427, 2.428, 2.429, 2.43, 2.431, 2.432, 2.433, 2.434, 2.435, 2.436, 2.437, 2.438, 2.439, 2.44, 2.441, 2.442, 2.443, 2.444, 2.445, 2.446, 2.447, 2.448, 2.449, 2.45, 2.451, 2.452, 2.453, 2.454, 2.455, 2.456, 2.457, 2.458, 2.459, 2.46, 2.461, 2.462, 2.463, 2.464, 2.465, 2.466, 2.467, 2.468, 2.469, 2.47, 2.471, 2.472, 2.473, 2.474, 2.475, 2.476, 2.477, 2.478, 2.479, 2.48, 2.481, 2.482, 2.483, 2.484, 2.485, 2.486, 2.487, 2.488, 2.489, 2.49, 2.491, 2.492, 2.493, 2.494, 2.495, 2.496, 2.497, 2.498, 2.499, 2.5, 2.501, 2.502, 2.503, 2.504, 2.505, 2.506, 2.507, 2.508, 2.509, 2.51, 2.511, 2.512, 2.513, 2.514, 2.515, 2.516, 2.517, 2.518, 2.519, 2.52, 2.521, 2.522, 2.523, 2.524, 2.525, 2.526, 2.527, 2.528, 2.529, 2.53, 2.531, 2.532, 2.533, 2.534, 2.535, 2.536, 2.537, 2.538, 2.539, 2.54, 2.541, 2.542, 2.543, 2.544, 2.545, 2.546, 2.547, 2.548, 2.549, 2.55, 2.551, 2.552, 2.553, 2.554, 2.555, 2.556, 2.557, 2.558, 2.559, 2.56, 2.561, 2.562, 2.563, 2.564, 2.565, 2.566, 2.567, 2.568, 2.569, 2.57, 2.571, 2.572, 2.573, 2.574, 2.575, 2.576, 2.577, 2.578, 2.579, 2.58, 2.581, 2.582, 2.583, 2.584, 2.585, 2.586, 2.587, 2.588, 2.589, 2.59, 2.591, 2.592, 2.593, 2.594, 2.595, 2.596, 2.597, 2.598, 2.599, 2.6, 2.601, 2.602, 2.603, 2.604, 2.605, 2.606, 2.607, 2.608, 2.609, 2.61, 2.611, 2.612, 2.613, 2.614, 2.615, 2.616, 2.617, 2.618, 2.619, 2.62, 2.621, 2.622, 2.623, 2.624, 2.625, 2.626, 2.627, 2.628, 2.629, 2.63, 2.631, 2.632, 2.633, 2.634, 2.635, 2.636, 2.637, 2.638, 2.639, 2.64, 2.641, 2.642, 2.643, 2.644, 2.645, 2.646, 2.647, 2.648, 2.649, 2.65, 2.651, 2.652, 2.653, 2.654, 2.655, 2.656, 2.657, 2.658, 2.659, 2.66, 2.661, 2.662, 2.663, 2.664, 2.665, 2.666, 2.667, 2.668, 2.669, 2.67, 2.671, 2.672, 2.673, 2.674, 2.675, 2.676, 2.677, 2.678, 2.679, 2.68, 2.681, 2.682, 2.683, 2.684, 2.685, 2.686, 2.687, 2.688, 2.689, 2.69, 2.691, 2.692, 2.693, 2.694, 2.695, 2.696, 2.697, 2.698, 2.699, 2.7, 2.701, 2.702, 2.703, 2.704, 2.705, 2.706, 2.707, 2.708, 2.709, 2.71, 2.711, 2.712, 2.713, 2.714, 2.715, 2.716, 2.717, 2.718, 2.719, 2.72, 2.721, 2.722, 2.723, 2.724, 2.725, 2.726, 2.727, 2.728, 2.729, 2.73, 2.731, 2.732, 2.733, 2.734, 2.735, 2.736, 2.737, 2.738, 2.739, 2.74, 2.741, 2.742, 2.743, 2.744, 2.745, 2.746, 2.747, 2.748, 2.749, 2.75, 2.751, 2.752, 2.753, 2.754, 2.755, 2.756, 2.757, 2.758, 2.759, 2.76, 2.761, 2.762, 2.763, 2.764, 2.765, 2.766, 2.767, 2.768, 2.769, 2.77, 2.771, 2.772, 2.773, 2.774, 2.775, 2.776, 2.777, 2.778, 2.779, 2.78, 2.781, 2.782, 2.783, 2.784, 2.785, 2.786, 2.787, 2.788, 2.789, 2.79, 2.791, 2.792, 2.793, 2.794, 2.795, 2.796, 2.797, 2.798, 2.799, 2.8, 2.801, 2.802, 2.803, 2.804, 2.805, 2.806, 2.807, 2.808, 2.809, 2.81, 2.811, 2.812, 2.813, 2.814, 2.815, 2.816, 2.817, 2.818, 2.819, 2.82, 2.821, 2.822, 2.823, 2.824, 2.825, 2.826, 2.827, 2.828, 2.829, 2.83, 2.831, 2.832, 2.833, 2.834, 2.835, 2.836, 2.837, 2.838, 2.839, 2.84, 2.841, 2.842, 2.843, 2.844, 2.845, 2.846, 2.847, 2.848, 2.849, 2.85, 2.851, 2.852, 2.853, 2.854, 2.855, 2.856, 2.857, 2.858, 2.859, 2.86, 2.861, 2.862, 2.863, 2.864, 2.865, 2.866, 2.867, 2.868, 2.869, 2.87, 2.871, 2.872, 2.873, 2.874, 2.875, 2.876, 2.877, 2.878, 2.879, 2.88, 2.881, 2.882, 2.883, 2.884, 2.885, 2.886, 2.887, 2.888, 2.889, 2.89, 2.891, 2.892, 2.893, 2.894, 2.895, 2.896, 2.897, 2.898, 2.899, 2.9, 2.901, 2.902, 2.903, 2.904, 2.905, 2.906, 2.907, 2.908, 2.909, 2.91, 2.911, 2.912, 2.913, 2.914, 2.915, 2.916, 2.917, 2.918, 2.919, 2.92, 2.921, 2.922, 2.923, 2.924, 2.925, 2.926, 2.927, 2.928, 2.929, 2.93, 2.931, 2.932, 2.933, 2.934, 2.935, 2.936, 2.937, 2.938, 2.939, 2.94, 2.941, 2.942, 2.943, 2.944, 2.945, 2.946, 2.947, 2.948, 2.949, 2.95, 2.951, 2.952, 2.953, 2.954, 2.955, 2.956, 2.957, 2.958, 2.959, 2.96, 2.961, 2.962, 2.963, 2.964, 2.965, 2.966, 2.967, 2.968, 2.969, 2.97, 2.971, 2.972, 2.973, 2.974, 2.975, 2.976, 2.977, 2.978, 2.979, 2.98, 2.981, 2.982, 2.983, 2.984, 2.985, 2.986, 2.987, 2.988, 2.989, 2.99, 2.991, 2.992, 2.993, 2.994, 2.995, 2.996, 2.997, 2.998, 2.999, 3, 3.001, 3.002, 3.003, 3.004, 3.005, 3.006, 3.007, 3.008, 3.009, 3.01, 3.011, 3.012, 3.013, 3.014, 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2.975, 2.976, 2.977, 2.978, 2.979, 2.98, 2.981, 2.982, 2.983, 2.984, 2.985, 2.986, 2.987, 2.988, 2.989, 2.99, 2.991, 2.992, 2.993, 2.994, 2.995, 2.996, 2.997, 2.998, 2.999, 3, 3.001, 3.002, 3.003, 3.004, 3.005, 3.006, 3.007, 3.008, 3.009, 3.01, 3.011, 3.012, 3.013, 3.014, 3.015, 3.016, 3.017, 3.018, 3.019, 3.02, 3.021, 3.022, 3.023, 3.024, 3.025, 3.026, 3.027, 3.028, 3.029, 3.03, 3.031, 3.032, 3.033, 3.034, 3.035, 3.036, 3.037, 3.038, 3.039, 3.04, 3.041, 3.042, 3.043, 3.044, 3.045, 3.046, 3.047, 3.048, 3.049, 3.05, 3.051, 3.052, 3.053, 3.054, 3.055, 3.056, 3.057, 3.058, 3.059, 3.06, 3.061, 3.062, 3.063, 3.064, 3.065, 3.066, 3.067, 3.068, 3.069, 3.07, 3.071, 3.072, 3.073, 3.074, 3.075, 3.076, 3.077, 3.078, 3.079, 3.08, 3.081, 3.082, 3.083, 3.084, 3.085, 3.086, 3.087, 3.088, 3.089, 3.09, 3.091, 3.092, 3.093, 3.094, 3.095, 3.096, 3.097, 3.098, 3.099, 3.1, 3.101, 3.102, 3.103, 3.104, 3.105, 3.106, 3.107, 3.108, 3.109, 3.11, 3.111, 3.112, 3.113, 3.114, 3.115, 3.116, 3.117, 3.118, 3.119, 3.12, 3.121, 3.122, 3.123, 3.124, 3.125, 3.126, 3.127, 3.128, 3.129, 3.13, 3.131, 3.132, 3.133, 3.134, 3.135, 3.136, 3.137, 3.138, 3.139, 3.14, 3.141, 3.142, 3.143, 3.144, 3.145, 3.146, 3.147, 3.148, 3.149, 3.15, 3.151, 3.152, 3.153, 3.154, 3.155, 3.156, 3.157, 3.158, 3.159, 3.16, 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, 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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, 3.451, 3.452, 3.453, 3.454, 3.455, 3.456, 3.457, 3.458, 3.459, 3.46, 3.461, 3.462, 3.463, 3.464, 3.465, 3.466, 3.467, 3.468, 3.469, 3.47, 3.471, 3.472, 3.473, 3.474, 3.475, 3.476, 3.477, 3.478, 3.479, 3.48, 3.481, 3.482, 3.483, 3.484, 3.485, 3.486, 3.487, 3.488, 3.489, 3.49, 3.491, 3.492, 3.493, 3.494, 3.495, 3.496, 3.497, 3.498, 3.499, 3.5, 3.501, 3.502, 3.503, 3.504, 3.505, 3.506, 3.507, 3.508, 3.509, 3.51, 3.511, 3.512, 3.513, 3.514, 3.515, 3.516, 3.517, 3.518, 3.519, 3.52, 3.521, 3.522, 3.523, 3.524, 3.525, 3.526, 3.527, 3.528, 3.529, 3.53, 3.531, 3.532, 3.533, 3.534, 3.535, 3.536, 3.537, 3.538, 3.539, 3.54, 3.541, 3.542, 3.543, 3.544, 3.545, 3.546, 3.547, 3.548, 3.549, 3.55, 3.551, 3.552, 3.553, 3.554, 3.555, 3.556, 3.557, 3.558, 3.559, 3.56, 3.561, 3.562, 3.563, 3.564, 3.565, 3.566, 3.567, 3.568, 3.569, 3.57, 3.571, 3.572, 3.573, 3.574, 3.575, 3.576, 3.577, 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, 3.868, 3.869, 3.87, 3.871, 3.872, 3.873, 3.874, 3.875, 3.876, 3.877, 3.878, 3.879, 3.88, 3.881, 3.882, 3.883, 3.884, 3.885, 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, 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, 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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, 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, 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, 4.321, 4.322, 4.323, 4.324, 4.325, 4.326, 4.327, 4.328, 4.329, 4.33, 4.331, 4.332, 4.333, 4.334, 4.335, 4.336, 4.337, 4.338, 4.339, 4.34, 4.341, 4.342, 4.343, 4.344, 4.345, 4.346, 4.347, 4.348, 4.349, 4.35, 4.351, 4.352, 4.353, 4.354, 4.355, 4.356, 4.357, 4.358, 4.359, 4.36, 4.361, 4.362, 4.363, 4.364, 4.365, 4.366, 4.367, 4.368, 4.369, 4.37, 4.371, 4.372, 4.373, 4.374, 4.375, 4.376, 4.377, 4.378, 4.379, 4.38, 4.381, 4.382, 4.383, 4.384, 4.385, 4.386, 4.387, 4.388, 4.389, 4.39, 4.391, 4.392, 4.393, 4.394, 4.395, 4.396, 4.397, 4.398, 4.399, 4.4, 4.401, 4.402, 4.403, 4.404, 4.405, 4.406, 4.407, 4.408, 4.409, 4.41, 4.411, 4.412, 4.413, 4.414, 4.415, 4.416, 4.417, 4.418, 4.419, 4.42, 4.421, 4.422, 4.423, 4.424, 4.425, 4.426, 4.427, 4.428, 4.429, 4.43, 4.431, 4.432, 4.433, 4.434, 4.435, 4.436, 4.437, 4.438, 4.439, 4.44, 4.441, 4.442, 4.443, 4.444, 4.445, 4.446, 4.447, 4.448, 4.449, 4.45, 4.451, 4.452, 4.453, 4.454, 4.455, 4.456, 4.457, 4.458, 4.459, 4.46, 4.461, 4.462, 4.463, 4.464, 4.465, 4.466, 4.467, 4.468, 4.469, 4.47, 4.471, 4.472, 4.473, 4.474, 4.475, 4.476, 4.477, 4.478, 4.479, 4.48, 4.481, 4.482, 4.483, 4.484, 4.485, 4.486, 4.487, 4.488, 4.489, 4.49, 4.491, 4.492, 4.493, 4.494, 4.495, 4.496, 4.497, 4.498, 4.499, 4.5, 4.501, 4.502, 4.503, 4.504, 4.505, 4.506, 4.507, 4.508, 4.509, 4.51, 4.511, 4.512, 4.513, 4.514, 4.515, 4.516, 4.517, 4.518, 4.519, 4.52, 4.521, 4.522, 4.523, 4.524, 4.525, 4.526, 4.527, 4.528, 4.529, 4.53, 4.531, 4.532, 4.533, 4.534, 4.535, 4.536, 4.537, 4.538, 4.539, 4.54, 4.541, 4.542, 4.543, 4.544, 4.545, 4.546, 4.547, 4.548, 4.549, 4.55, 4.551, 4.552, 4.553, 4.554, 4.555, 4.556, 4.557, 4.558, 4.559, 4.56, 4.561, 4.562, 4.563, 4.564, 4.565, 4.566, 4.567, 4.568, 4.569, 4.57, 4.571, 4.572, 4.573, 4.574, 4.575, 4.576, 4.577, 4.578, 4.579, 4.58, 4.581, 4.582, 4.583, 4.584, 4.585, 4.586, 4.587, 4.588, 4.589, 4.59, 4.591, 4.592, 4.593, 4.594, 4.595, 4.596, 4.597, 4.598, 4.599, 4.6, 4.601, 4.602, 4.603, 4.604, 4.605, 4.606, 4.607, 4.608, 4.609, 4.61, 4.611, 4.612, 4.613, 4.614, 4.615, 4.616, 4.617, 4.618, 4.619, 4.62, 4.621, 4.622, 4.623, 4.624, 4.625, 4.626, 4.627, 4.628, 4.629, 4.63, 4.631, 4.632, 4.633, 4.634, 4.635, 4.636, 4.637, 4.638, 4.639, 4.64, 4.641, 4.642, 4.643, 4.644, 4.645, 4.646, 4.647, 4.648, 4.649, 4.65, 4.651, 4.652, 4.653, 4.654, 4.655, 4.656, 4.657, 4.658, 4.659, 4.66, 4.661, 4.662, 4.663, 4.664, 4.665, 4.666, 4.667, 4.668, 4.669, 4.67, 4.671, 4.672, 4.673, 4.674, 4.675, 4.676, 4.677, 4.678, 4.679, 4.68, 4.681, 4.682, 4.683, 4.684, 4.685, 4.686, 4.687, 4.688, 4.689, 4.69, 4.691, 4.692, 4.693, 4.694, 4.695, 4.696, 4.697, 4.698, 4.699, 4.7, 4.701, 4.702, 4.703, 4.704, 4.705, 4.706, 4.707, 4.708, 4.709, 4.71, 4.711, 4.712, 4.713, 4.714, 4.715, 4.716, 4.717, 4.718, 4.719, 4.72, 4.721, 4.722, 4.723, 4.724, 4.725, 4.726, 4.727, 4.728, 4.729, 4.73, 4.731, 4.732, 4.733, 4.734, 4.735, 4.736, 4.737, 4.738, 4.739, 4.74, 4.741, 4.742, 4.743, 4.744, 4.745, 4.746, 4.747, 4.748, 4.749, 4.75, 4.751, 4.752, 4.753, 4.754, 4.755, 4.756, 4.757, 4.758, 4.759, 4.76, 4.761, 4.762, 4.763, 4.764, 4.765, 4.766, 4.767, 4.768, 4.769, 4.77, 4.771, 4.772, 4.773, 4.774, 4.775, 4.776, 4.777, 4.778, 4.779, 4.78, 4.781, 4.782, 4.783, 4.784, 4.785, 4.786, 4.787, 4.788, 4.789, 4.79, 4.791, 4.792, 4.793, 4.794, 4.795, 4.796, 4.797, 4.798, 4.799, 4.8, 4.801, 4.802, 4.803, 4.804, 4.805, 4.806, 4.807, 4.808, 4.809, 4.81, 4.811, 4.812, 4.813, 4.814, 4.815, 4.816, 4.817, 4.818, 4.819, 4.82, 4.821, 4.822, 4.823, 4.824, 4.825, 4.826, 4.827, 4.828, 4.829, 4.83, 4.831, 4.832, 4.833, 4.834, 4.835, 4.836, 4.837, 4.838, 4.839, 4.84, 4.841, 4.842, 4.843, 4.844, 4.845, 4.846, 4.847, 4.848, 4.849, 4.85, 4.851, 4.852, 4.853, 4.854, 4.855, 4.856, 4.857, 4.858, 4.859, 4.86, 4.861, 4.862, 4.863, 4.864, 4.865, 4.866, 4.867, 4.868, 4.869, 4.87, 4.871, 4.872, 4.873, 4.874, 4.875, 4.876, 4.877, 4.878, 4.879, 4.88, 4.881, 4.882, 4.883, 4.884, 4.885, 4.886, 4.887, 4.888, 4.889, 4.89, 4.891, 4.892, 4.893, 4.894, 4.895, 4.896, 4.897, 4.898, 4.899, 4.9, 4.901, 4.902, 4.903, 4.904, 4.905, 4.906, 4.907, 4.908, 4.909, 4.91, 4.911, 4.912, 4.913, 4.914, 4.915, 4.916, 4.917, 4.918, 4.919, 4.92, 4.921, 4.922, 4.923, 4.924, 4.925, 4.926, 4.927, 4.928, 4.929, 4.93, 4.931, 4.932, 4.933, 4.934, 4.935, 4.936, 4.937, 4.938, 4.939, 4.94, 4.941, 4.942, 4.943, 4.944, 4.945, 4.946, 4.947, 4.948, 4.949, 4.95, 4.951, 4.952, 4.953, 4.954, 4.955, 4.956, 4.957, 4.958, 4.959, 4.96, 4.961, 4.962, 4.963, 4.964, 4.965, 4.966, 4.967, 4.968, 4.969, 4.97, 4.971, 4.972, 4.973, 4.974, 4.975, 4.976, 4.977, 4.978, 4.979, 4.98, 4.981, 4.982, 4.983, 4.984, 4.985, 4.986, 4.987, 4.988, 4.989, 4.99, 4.991, 4.992, 4.993, 4.994, 4.995, 4.996, 4.997, 4.998, 4.999, 5, 5.001, 5.002, 5.003, 5.004, 5.005, 5.006, 5.007, 5.008, 5.009, 5.01, 5.011, 5.012, 5.013, 5.014, 5.015, 5.016, 5.017, 5.018, 5.019, 5.02, 5.021, 5.022, 5.023, 5.024, 5.025, 5.026, 5.027, 5.028, 5.029, 5.03, 5.031, 5.032, 5.033, 5.034, 5.035, 5.036, 5.037, 5.038, 5.039, 5.04, 5.041, 5.042, 5.043, 5.044, 5.045, 5.046, 5.047, 5.048, 5.049, 5.05, 5.051, 5.052, 5.053, 5.054, 5.055, 5.056, 5.057, 5.058, 5.059, 5.06, 5.061, 5.062, 5.063, 5.064, 5.065, 5.066, 5.067, 5.068, 5.069, 5.07, 5.071, 5.072, 5.073, 5.074, 5.075, 5.076, 5.077, 5.078, 5.079, 5.08, 5.081, 5.082, 5.083, 5.084, 5.085, 5.086, 5.087, 5.088, 5.089, 5.09, 5.091, 5.092, 5.093, 5.094, 5.095, 5.096, 5.097, 5.098, 5.099, 5.1, 5.101, 5.102, 5.103, 5.104, 5.105, 5.106, 5.107, 5.108, 5.109, 5.11, 5.111, 5.112, 5.113, 5.114, 5.115, 5.116, 5.117, 5.118, 5.119, 5.12, 5.121, 5.122, 5.123, 5.124, 5.125, 5.126, 5.127, 5.128, 5.129, 5.13, 5.131, 5.132, 5.133, 5.134, 5.135, 5.136, 5.137, 5.138, 5.139, 5.14, 5.141, 5.142, 5.143, 5.144, 5.145, 5.146, 5.147, 5.148, 5.149, 5.15, 5.151, 5.152, 5.153, 5.154, 5.155, 5.156, 5.157, 5.158, 5.159, 5.16, 5.161, 5.162, 5.163, 5.164, 5.165, 5.166, 5.167, 5.168, 5.169, 5.17, 5.171, 5.172, 5.173, 5.174, 5.175, 5.176, 5.177, 5.178, 5.179, 5.18, 5.181, 5.182, 5.183, 5.184, 5.185, 5.186, 5.187, 5.188, 5.189, 5.19, 5.191, 5.192, 5.193, 5.194, 5.195, 5.196, 5.197, 5.198, 5.199, 5.2, 5.201, 5.202, 5.203, 5.204, 5.205, 5.206, 5.207, 5.208, 5.209, 5.21, 5.211, 5.212, 5.213, 5.214, 5.215, 5.216, 5.217, 5.218, 5.219, 5.22, 5.221, 5.222, 5.223, 5.224, 5.225, 5.226, 5.227, 5.228, 5.229, 5.23, 5.231, 5.232, 5.233, 5.234, 5.235, 5.236, 5.237, 5.238, 5.239, 5.24, 5.241, 5.242, 5.243, 5.244, 5.245, 5.246, 5.247, 5.248, 5.249, 5.25, 5.251, 5.252, 5.253, 5.254, 5.255, 5.256, 5.257, 5.258, 5.259, 5.26, 5.261, 5.262, 5.263, 5.264, 5.265, 5.266, 5.267, 5.268, 5.269, 5.27, 5.271, 5.272, 5.273, 5.274, 5.275, 5.276, 5.277, 5.278, 5.279, 5.28, 5.281, 5.282, 5.283, 5.284, 5.285, 5.286, 5.287, 5.288, 5.289, 5.29, 5.291, 5.292, 5.293, 5.294, 5.295, 5.296, 5.297, 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Модель 1D динамики простой механической системы: модель взаимодействия материальной точки с поверхностью земли при падении под действием гравитации
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engee
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