Задача №12.33

Условие

Точка M движется по линии пересечения сферы x2+y2+z2=R2 и цилиндра (x-R/2)2+y2=R2/4. Уравнения движения точки в сферических координатах имеют вид (см. задачу 10.21)
r = R, φ = kt/2, θ = kt/2. Найти проекции и модуль ускорения точки в сферических координатах.

Решение




Предыдущая задача №32
Точка M движется по винтовой линии. Уравнения движения ее в цилиндрической системе координат имеют вид
r = a, φ = kt, z = νt. Найти проекции ускорения точки на оси цилиндрической системы координат, касательную и нормальную составляющие ускорения и радиус кривизны винтовой линии.
Следующая задача №34
Корабль движется под постоянным курсовым углом α к географическому меридиану, описывая при этом локсодромию (см. задачу 11.13). Считая, что модуль скорости v корабля не изменяется, определить проекции ускорения корабля на оси сферических координат r, λ и φ (λ — долгота, φ — широта места плавания), модуль ускорения и радиус кривизны локсодромии.
Источник: Решебник Мещерского 12 класс
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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
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2.10
2.11
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3.1
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3.3
3.4
3.5
3.6
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4.1
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5.1
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6.1
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7.1
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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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15.1
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16.1
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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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24.1
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24.34
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25.1
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26.1
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27.1
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28.1
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29.1
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30.1
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31.1
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31.35
32.1
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32.86
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32.107
33.1
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34.1
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35.1
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36.1
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37.1
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38.1
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39.1
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40.1
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41.1
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42.1
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43.1
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44.1
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45.3
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46.1
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47.1
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48.1
48.5
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48.38
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48.44
48.48
48.49
49.1
49.2
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53.5
53.12
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54.1
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54.18
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54.32
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54.35
55.2
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55.25
55.38
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56.3
56.7
56.9
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