Задача №20.1
Условие
Искусственная горизонтальная площадка на качающемся корабле создается с помощью карданова подвеса. Ось y1 вращения внешнего кольца параллельна продольной оси корабля; угол поворота внешнего кольца обозначается через β (угол бортовой качки). Угол поворота внутренней рамки обозначается через α. Для ориентации колец вводят три системы координат: система ξηζ связана с кораблем (ось ξ направлена к правому борту, ось η — к носу корабля, ось ζ — перпендикулярна палубе); система x1y1z1 связана с внешним кольцом (ось y1 совпадает с осью η); система xyz связана с внутренним кольцом (ось x совпадает с x1). Положительные направления отсчета углов видны из рисунков; при α=β=0 все системы отсчета совпадают. Определить ориентацию (соответствующие направляющие косинусы) внутреннего кольца подвеса относительно корабля.Решение
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1.1
1.2
1.3
1.4
1.5
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
2.12
2.13
2.14
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2.17
2.18
2.19
2.20
2.21
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2.24
2.25
2.26
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2.28
2.29
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2.31
2.32
2.33
2.34
2.35
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2.37
2.38
2.39
2.40
2.41
2.42
2.43
2.44
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2.46
2.47
2.48
2.49
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2.53
2.54
2.55
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
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3.11
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3.13
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3.20
3.21
3.22
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4.1
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5.1
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6.1
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8.1
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9.1
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10.1
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11.1
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12.1
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13.1
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14.1
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17.1
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18.1
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19.1
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20.1
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21.2
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22.1
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23.1
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23.71
24.1
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24.34
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25.1
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26.1
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26.4
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26.34
26.35
27.1
27.2
27.3
27.4
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27.6
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27.12
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27.20
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27.32
27.33
27.34
27.35
27.36
27.37
27.38
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27.40
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27.42
27.43
27.44
27.45
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27.47
27.48
27.49
27.50
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27.54
27.55
27.58
27.59
27.60
27.61
27.62
27.63
27.64
27.65
28.1
28.2
28.3
28.4
28.5
28.6
28.7
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28.10
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28.22
29.1
29.2
29.3
29.4
29.5
29.6
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30.1
30.2
30.3
30.4
30.5
30.6
30.7
30.8
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30.11
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31.1
31.2
31.3
31.4
31.5
31.6
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31.8
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31.11
31.13
31.14
31.15
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31.25
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31.32
31.33
31.34
31.35
32.1
32.2
32.3
32.4
32.5
32.6
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32.8
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32.10
32.11
32.12
32.13
32.14
32.15
32.16
32.17
32.18
32.19
32.20
32.21
32.22
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32.24
32.25
32.26
32.27
32.28
32.29
32.30
32.31
32.32
32.33
32.34
32.35
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32.37
32.38
32.39
32.40
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32.42
32.43
32.44
32.45
32.46
32.47
32.48
32.49
32.50
32.51
32.52
32.53
32.54
32.55
32.56
32.57
32.58
32.59
32.60
32.61
32.62
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32.64
32.65
32.66
32.67
32.68
32.69
32.70
32.71
32.72
32.73
32.74
32.75
32.76
32.77
32.79
32.80
32.81
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32.84
32.85
32.86
32.87
32.88
32.89
32.90
32.91
32.92
32.93
32.94
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32.96
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32.100
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32.102
32.103
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32.105
32.106
32.107
33.1
33.2
33.3
33.4
33.5
33.6
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33.22
34.1
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34.6
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34.31
35.1
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36.1
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37.1
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37.59
38.1
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38.33
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38.38
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38.53
39.1
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40.1
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41.1
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42.1
42.2
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42.5
42.6
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43.1
43.2
43.3
43.4
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44.1
44.2
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45.3
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45.37
46.1
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46.6
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46.32
47.1
47.2
47.3
47.4
47.5
47.6
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48.1
48.5
48.6
48.7
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48.12
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48.23
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48.27
48.28
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48.31
48.33
48.34
48.35
48.38
48.40
48.41
48.42
48.43
48.44
48.48
48.49
49.1
49.2
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49.4
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49.16
53.5
53.12
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54.1
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54.18
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54.22
54.32
54.33
54.35
55.2
55.3
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55.21
55.25
55.38
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55.44
56.3
56.7
56.9