
- •«Исследование свойств траекторий движения неуправляемого ла на пассивном участке»
- •Содержание
- •Задание
- •Математическая постановка задачи
- •Исходные данные
- •Графики изменения основных элементов траектории
- •Методы определения угла максимальной дальности и угла бросания, обеспечивающего заданную дальность.
- •Описание метода половинного деления
- •Алгоритм метода половинного деления
- •Анализ результатов
Исходные данные
Вариант 7.
;
;
;
;
.
Таблицы результатов расчета траекторий
Таблица 3.1. Расчет
координат Х, У, и скорости при начальном
угле бросания
|
||||
|
|
|
|
|
0 |
84 |
12 |
0 |
0 |
0.1 |
100.775 |
11.403 |
9.047 |
1.871 |
0.2 |
117.694 |
10.897 |
19.765 |
3.981 |
0.3 |
134.757 |
10.459 |
32.169 |
6.317 |
0.4 |
151.962 |
10.073 |
46.276 |
8.871 |
0.5 |
169.31 |
9.728 |
62.101 |
11.631 |
0.6 |
186.8 |
9.417 |
79.659 |
14.59 |
0.7 |
204.426 |
9.133 |
98.965 |
17.741 |
0.8 |
222.172 |
8.873 |
120.033 |
21.078 |
0.9 |
240.026 |
8.632 |
142.874 |
24.593 |
1 |
257.975 |
8.409 |
167.5 |
28.281 |
1.1 |
275.998 |
8.201 |
193.92 |
32.137 |
1.2 |
294.071 |
8.005 |
222.14 |
36.154 |
1.3 |
312.169 |
7.822 |
252.165 |
40.326 |
1.4 |
330.27 |
7.648 |
283.996 |
44.649 |
1.5 |
348.348 |
7.484 |
317.633 |
49.116 |
1.6 |
366.41 |
7.328 |
353.075 |
53.722 |
1.7 |
384.533 |
7.18 |
390.322 |
58.462 |
1.8 |
402.73 |
7.038 |
429.384 |
63.333 |
1.9 |
420.997 |
6.903 |
470.267 |
68.331 |
2 |
439.336 |
6.773 |
512.978 |
73.452 |
2.1 |
457.748 |
6.649 |
557.526 |
78.693 |
2.2 |
476.232 |
6.529 |
603.918 |
84.05 |
2.3 |
494.791 |
6.414 |
652.161 |
89.522 |
2.4 |
513.426 |
6.303 |
702.263 |
95.105 |
2.5 |
532.141 |
6.196 |
754.231 |
100.795 |
2.6 |
550.938 |
6.093 |
808.075 |
106.592 |
2.7 |
569.82 |
5.994 |
863.803 |
112.491 |
2.8 |
588.792 |
5.897 |
921.423 |
118.491 |
2.9 |
607.86 |
5.804 |
980.945 |
124.589 |
3 |
627.027 |
5.713 |
1042.378 |
130.784 |
3.1 |
646.301 |
5.625 |
1105.734 |
137.072 |
3.2 |
665.688 |
5.54 |
1171.024 |
143.454 |
3.3 |
685.197 |
5.457 |
1238.258 |
149.925 |
3.4 |
704.836 |
5.377 |
1307.45 |
156.486 |
4.4 |
554.245 |
4.479 |
1931.175 |
210.658 |
5.4 |
442.935 |
3.343 |
2425.608 |
244.827 |
6.4 |
362.207 |
1.937 |
2825.614 |
263.6 |
7.4 |
309.117 |
0.247 |
3158.678 |
270.207 |
8.4 |
277.255 |
-1.679 |
3450.667 |
266.736 |
9.4 |
255.725 |
-3.79 |
3716.237 |
254.183 |
10.4 |
239.863 |
-6.053 |
3962.747 |
233.057 |
11.4 |
227.613 |
-8.441 |
4194.367 |
203.685 |
12.4 |
217.894 |
-10.929 |
4413.762 |
166.309 |
13.4 |
210.066 |
-13.497 |
4622.757 |
121.124 |
14.4 |
203.72 |
-16.124 |
4822.662 |
68.308 |
15.4 |
198.576 |
-18.79 |
5014.45 |
8.026 |
15.5 |
198.119 |
-19.058 |
5033.213 |
1.593 |
15.524 |
198.01 |
-19.123 |
5037.79 |
0 |
Таблица 3.2. Расчет координат Х, У, и скорости при начальном угле бросания 38 градусов.
t, c |
V, м/с |
Teta, град |
Х, м |
У, м |
|
0 |
84 |
38 |
0 |
0 |
|
0.1 |
100.374 |
37.517 |
7.29 |
5.643 |
|
0.2 |
116.89 |
37.105 |
15.931 |
12.226 |
|
0.3 |
133.548 |
36.745 |
25.942 |
19.748 |
|
0.4 |
150.348 |
36.427 |
37.341 |
28.207 |
|
0.5 |
167.291 |
36.142 |
50.144 |
37.605 |
|
0.6 |
184.376 |
35.883 |
64.368 |
47.942 |
|
0.7 |
201.6 |
35.647 |
80.029 |
59.22 |
|
0.8 |
218.948 |
35.429 |
97.14 |
71.442 |
|
0.9 |
236.409 |
35.228 |
115.716 |
84.607 |
|
1 |
253.972 |
35.04 |
135.769 |
98.717 |
|
1.1 |
271.618 |
34.865 |
157.31 |
113.772 |
|
1.2 |
289.325 |
34.7 |
180.347 |
129.772 |
|
1.3 |
307.07 |
34.545 |
204.887 |
146.714 |
|
1.4 |
324.833 |
34.399 |
230.936 |
164.597 |
|
1.5 |
342.589 |
34.26 |
258.496 |
183.417 |
|
1.6 |
360.329 |
34.127 |
287.568 |
203.169 |
|
1.7 |
378.116 |
34.001 |
318.156 |
223.85 |
|
1.8 |
395.992 |
33.881 |
350.268 |
245.46 |
|
1.9 |
413.951 |
33.766 |
383.912 |
268.002 |
|
2 |
431.993 |
33.655 |
419.098 |
291.477 |
|
2.1 |
450.121 |
33.549 |
455.835 |
315.886 |
|
2.2 |
468.336 |
33.447 |
494.132 |
341.231 |
|
2.3 |
486.64 |
33.349 |
533.997 |
367.514 |
|
2.4 |
505.037 |
33.254 |
575.44 |
394.738 |
|
2.5 |
523.53 |
33.162 |
618.47 |
422.904 |
|
2.6 |
542.123 |
33.074 |
663.098 |
452.016 |
|
2.7 |
560.821 |
32.989 |
709.333 |
482.077 |
|
2.8 |
579.628 |
32.906 |
757.185 |
513.089 |
|
2.9 |
598.552 |
32.826 |
806.666 |
545.058 |
|
3 |
617.598 |
32.748 |
857.787 |
577.986 |
|
3.1 |
636.775 |
32.673 |
910.561 |
611.879 |
|
3.2 |
656.09 |
32.6 |
964.998 |
646.741 |
|
3.3 |
675.552 |
32.529 |
1021.114 |
682.579 |
|
3.4 |
695.172 |
32.459 |
1078.921 |
719.397 |
|
4.4 |
552.403 |
31.688 |
1604.451 |
1049.107 |
|
5.4 |
446.756 |
30.718 |
2029.261 |
1306.768 |
|
6.4 |
369.074 |
29.518 |
2380.276 |
1510.711 |
|
7.4 |
314.109 |
28.064 |
2677.607 |
1674.384 |
|
8.4 |
279.582 |
26.374 |
2940.445 |
1809.776 |
|
9.4 |
255.555 |
24.472 |
3181.46 |
1924.496 |
|
10.4 |
237.342 |
22.378 |
3407.196 |
2022.431 |
|
11.4 |
222.784 |
20.1 |
3621.347 |
2105.777 |
|
12.4 |
210.787 |
17.646 |
3826.258 |
2175.929 |
|
13.4 |
200.718 |
15.026 |
4023.526 |
2233.84 |
|
14.4 |
192.187 |
12.246 |
4214.291 |
2280.198 |
|
15.4 |
184.94 |
9.32 |
4399.395 |
2315.522 |
|
16.4 |
178.769 |
6.26 |
4579.467 |
2340.217 |
|
17.4 |
173.45 |
3.081 |
4754.897 |
2354.601 |
|
18.4 |
168.936 |
-0.199 |
4925.945 |
2358.948 |
|
19.4 |
165.192 |
-3.559 |
5092.834 |
2353.509 |
|
20.4 |
162.186 |
-6.975 |
5255.75 |
2338.516 |
|
21.4 |
159.88 |
-10.422 |
5414.853 |
2314.189 |
|
22.4 |
158.237 |
-13.874 |
5570.275 |
2280.739 |
|
23.4 |
157.212 |
-17.303 |
5722.126 |
2238.37 |
|
24.4 |
156.761 |
-20.686 |
5870.497 |
2187.286 |
|
25.4 |
156.834 |
-23.998 |
6015.458 |
2127.689 |
|
26.4 |
157.38 |
-27.221 |
6157.068 |
2059.784 |
|
27.4 |
158.345 |
-30.339 |
6295.369 |
1983.78 |
|
28.4 |
159.676 |
-33.339 |
6430.396 |
1899.892 |
|
29.4 |
161.32 |
-36.213 |
6562.173 |
1808.342 |
|
30.4 |
163.225 |
-38.955 |
6690.716 |
1709.359 |
|
31.4 |
165.342 |
-41.564 |
6816.038 |
1603.18 |
|
32.4 |
167.623 |
-44.038 |
6938.144 |
1490.05 |
|
33.4 |
170.024 |
-46.382 |
7057.04 |
1370.224 |
|
34.4 |
172.504 |
-48.597 |
7172.728 |
1243.961 |
|
35.4 |
175.025 |
-50.69 |
7285.211 |
1111.531 |
|
36.4 |
177.554 |
-52.665 |
7394.492 |
973.21 |
|
37.4 |
180.06 |
-54.529 |
7500.576 |
829.277 |
|
38.4 |
182.515 |
-56.288 |
7603.468 |
680.02 |
|
39.4 |
184.897 |
-57.948 |
7703.179 |
525.728 |
|
40.4 |
187.185 |
-59.515 |
7799.72 |
366.693 |
|
41.4 |
189.312 |
-60.995 |
7893.099 |
203.225 |
|
42.4 |
191.243 |
-62.395 |
7983.305 |
35.676 |
|
42.61 |
191.624 |
-62.679 |
8001.844 |
0 |
Таблица 3.3. Расчет координат Х, У, и скорости при начальном угле бросания 65 градусов.
t,c |
V, м/с |
Teta, град |
Х, м |
У, м |
0 |
84 |
70 |
0 |
0 |
0.1 |
100.054 |
69.79 |
3.164 |
8.642 |
0.2 |
116.246 |
69.609 |
6.917 |
18.785 |
0.3 |
132.576 |
69.451 |
11.269 |
30.44 |
0.4 |
149.047 |
69.31 |
16.229 |
43.619 |
0.5 |
165.658 |
69.183 |
21.805 |
58.333 |
0.6 |
182.411 |
69.068 |
28.007 |
74.594 |
0.7 |
199.302 |
68.963 |
34.842 |
92.414 |
0.8 |
216.32 |
68.866 |
42.319 |
111.804 |
0.9 |
233.453 |
68.775 |
50.445 |
132.773 |
1 |
250.692 |
68.691 |
59.226 |
155.333 |
1.1 |
268.02 |
68.612 |
68.668 |
179.489 |
1.2 |
285.417 |
68.538 |
78.777 |
205.249 |
1.3 |
302.862 |
68.468 |
89.557 |
232.618 |
1.4 |
320.335 |
68.402 |
101.011 |
261.598 |
1.5 |
337.814 |
68.339 |
113.142 |
292.189 |
1.6 |
355.282 |
68.279 |
125.951 |
324.391 |
1.7 |
372.785 |
68.222 |
139.441 |
358.204 |
1.8 |
390.384 |
68.167 |
153.616 |
393.633 |
1.9 |
408.073 |
68.114 |
168.482 |
430.686 |
2 |
425.855 |
68.064 |
184.042 |
469.371 |
2.1 |
443.732 |
68.016 |
200.302 |
509.696 |
2.2 |
461.706 |
67.969 |
217.267 |
551.67 |
2.3 |
479.781 |
67.925 |
234.943 |
595.3 |
2.4 |
497.961 |
67.881 |
253.334 |
640.597 |
2.5 |
516.25 |
67.84 |
272.445 |
687.569 |
2.6 |
534.652 |
67.799 |
292.283 |
736.226 |
2.7 |
553.173 |
67.76 |
312.853 |
786.579 |
2.8 |
571.82 |
67.722 |
334.161 |
838.637 |
2.9 |
590.598 |
67.686 |
356.212 |
892.414 |
3 |
609.517 |
67.65 |
379.013 |
947.919 |
3.1 |
628.584 |
67.616 |
402.571 |
1005.167 |
3.2 |
647.808 |
67.582 |
426.893 |
1064.171 |
3.3 |
667.199 |
67.549 |
451.986 |
1124.945 |
3.4 |
686.769 |
67.518 |
477.857 |
1187.506 |
4.4 |
549.881 |
67.165 |
714.642 |
1755.079 |
5.4 |
448.593 |
66.72 |
909.044 |
2212.13 |
6.4 |
373.27 |
66.171 |
1072.429 |
2587.227 |
7.4 |
317.549 |
65.5 |
1212.998 |
2900.808 |
8.4 |
280.69 |
64.706 |
1338.349 |
3171.118 |
9.4 |
254.143 |
63.792 |
1454.188 |
3411.45 |
10.4 |
233.262 |
62.754 |
1563.565 |
3628.831 |
11.4 |
215.808 |
61.585 |
1668.218 |
3827.223 |
12.4 |
200.647 |
60.274 |
1769.248 |
4009.112 |
13.4 |
187.121 |
58.806 |
1867.408 |
4176.17 |
14.4 |
174.813 |
57.161 |
1963.236 |
4329.574 |
15.4 |
163.302 |
55.316 |
2057.083 |
4470.114 |
16.4 |
152.455 |
53.24 |
2149.154 |
4598.29 |
17.4 |
142.241 |
50.898 |
2239.618 |
4714.52 |
18.4 |
132.644 |
48.25 |
2328.626 |
4819.165 |
19.4 |
123.669 |
45.249 |
2416.313 |
4912.535 |
20.4 |
115.335 |
41.845 |
2502.797 |
4994.9 |
21.4 |
107.68 |
37.984 |
2588.185 |
5066.489 |
22.4 |
100.761 |
33.616 |
2672.569 |
5127.501 |
23.4 |
94.653 |
28.7 |
2756.031 |
5178.108 |
24.4 |
89.447 |
23.218 |
2838.64 |
5218.457 |
25.4 |
85.24 |
17.187 |
2920.454 |
5248.673 |
26.4 |
82.127 |
10.677 |
3001.521 |
5268.866 |
27.4 |
80.185 |
3.815 |
3081.875 |
5279.135 |
28.4 |
79.451 |
-3.217 |
3161.54 |
5279.566 |
29.4 |
79.918 |
-10.212 |
3240.529 |
5270.246 |
30.4 |
81.523 |
-16.971 |
3318.843 |
5251.256 |
31.4 |
84.163 |
-23.33 |
3396.472 |
5222.686 |
32.4 |
87.702 |
-29.186 |
3473.398 |
5184.628 |
33.4 |
91.996 |
-34.491 |
3549.597 |
5137.187 |
34.4 |
96.901 |
-39.243 |
3625.036 |
5080.478 |
35.4 |
102.285 |
-43.471 |
3699.678 |
5014.63 |
36.4 |
108.029 |
-47.221 |
3773.482 |
4939.786 |
37.4 |
114.031 |
-50.543 |
3846.404 |
4856.105 |
38.4 |
120.203 |
-53.491 |
3918.399 |
4763.76 |
39.4 |
126.473 |
-56.113 |
3989.419 |
4662.941 |
40.4 |
132.776 |
-58.452 |
4059.417 |
4553.852 |
41.4 |
139.059 |
-60.546 |
4128.346 |
4436.714 |
42.4 |
145.276 |
-62.43 |
4196.159 |
4311.761 |
43.4 |
151.388 |
-64.13 |
4262.809 |
4179.241 |
44.4 |
157.36 |
-65.672 |
4328.254 |
4039.416 |
45.4 |
163.164 |
-67.075 |
4392.449 |
3892.561 |
46.4 |
168.773 |
-68.357 |
4455.356 |
3738.961 |
47.4 |
174.167 |
-69.532 |
4516.934 |
3578.913 |
48.4 |
179.326 |
-70.614 |
4577.15 |
3412.721 |
49.4 |
184.193 |
-71.614 |
4635.968 |
3240.71 |
50.4 |
188.663 |
-72.54 |
4693.327 |
3063.292 |
51.4 |
192.724 |
-73.402 |
4749.162 |
2880.922 |
52.4 |
196.369 |
-74.206 |
4803.417 |
2694.06 |
53.4 |
199.602 |
-74.96 |
4856.043 |
2503.162 |
54.4 |
202.431 |
-75.668 |
4906.999 |
2308.678 |
55.4 |
204.873 |
-76.335 |
4956.258 |
2111.042 |
56.4 |
206.945 |
-76.964 |
5003.8 |
1910.668 |
57.4 |
208.671 |
-77.56 |
5049.616 |
1707.946 |
58.4 |
210.077 |
-78.125 |
5093.708 |
1503.242 |
59.4 |
211.189 |
-78.661 |
5136.085 |
1296.893 |
60.4 |
212.035 |
-79.171 |
5176.764 |
1089.206 |
61.4 |
212.642 |
-79.657 |
5215.77 |
880.462 |
62.4 |
213.035 |
-80.12 |
5253.134 |
670.912 |
63.4 |
213.24 |
-80.562 |
5288.891 |
460.781 |
64.4 |
213.278 |
-80.985 |
5323.082 |
250.268 |
65.4 |
213.17 |
-81.388 |
5355.75 |
39.551 |
65.588 |
213.136 |
-81.462 |
5361.712 |
0 |