Механика.Методика решения задач
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ȼ.ɋ. Ɋɭɫɚɤɨɜ, Ⱥ.ɂ. ɋɥɟɩɤɨɜ ȿ.Ⱥ. ɇɢɤɚɧɨɪɨɜɚ, ɇ.ɂ. ɑɢɫɬɹɤɨɜɚ
ɆȿɏȺɇɂɄȺ. ɆȿɌɈȾɂɄȺ Ɋȿɒȿɇɂə ɁȺȾȺɑ
Ⱦɨɩɭɳɟɧɨ ɍɆɈ ɩɨ ɤɥɚɫɫɢɱɟɫɤɨɦɭ ɭɧɢɜɟɪɫɢɬɟɬɫɤɨɦɭ ɨɛɪɚɡɨɜɚɧɢɸ ɊɎ ɜ ɤɚɱɟɫɬɜɟ ɭɱɟɛɧɨɝɨ ɩɨɫɨɛɢɹ ɞɥɹ ɫɬɭɞɟɧɬɨɜ ɜɵɫɲɢɯ ɭɱɟɛɧɵɯ ɡɚɜɟɞɟɧɢɣ, ɨɛɭɱɚɸɳɢɯɫɹ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ 010700.62 «Ɏɢɡɢɤɚ»
ɢ ɩɨ ɫɩɟɰɢɚɥɶɧɨɫɬɢ 010701.65 «Ɏɢɡɢɤɚ»
Ɇɨɫɤɜɚ Ɏɢɡɢɱɟɫɤɢɣ ɮɚɤɭɥɶɬɟɬ ɆȽɍ ɢɦ. Ɇ.ȼ. Ʌɨɦɨɧɨɫɨɜɚ
2010
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ȼ. ɋ. Ɋ ɭ ɫ ɚ ɤ ɨ ɜ , Ⱥ. ɂ. ɋ ɥ ɟ ɩ ɤ ɨ ɜ , ȿ. Ⱥ . ɇ ɢ ɤ ɚ ɧ ɨ ɪ ɨ ɜ ɚ ,
ɇ. ɂ. ɑ ɢ ɫ ɬ ɹ ɤ ɨ ɜ ɚ . Ɇɟɯɚɧɢɤɚ. Ɇɟɬɨɞɢɤɚ ɪɟɲɟɧɢɹ ɡɚɞɚɱ / ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ. Ɇ.: Ɏɢɡɢɱɟɫɤɢɣ ɮɚɤɭɥɶɬɟɬ ɆȽɍ, 2010. 368 ɫ.
ISBN 978-5-8279-0084-9
ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ ɩɨ ɪɟɲɟɧɢɸ ɡɚɞɚɱ ɦɟɯɚɧɢɤɢ ɧɚɩɢɫɚɧɨ ɧɚ ɨɫɧɨɜɚɧɢɢ ɦɧɨɝɨɥɟɬɧɟɝɨ ɨɩɵɬɚ ɩɪɨɜɟɞɟɧɢɹ ɡɚɧɹɬɢɣ ɩɨ ɮɢɡɢɤɟ ɧɚ ɮɢɡɢɱɟɫɤɨɦ ɮɚɤɭɥɶɬɟɬɟ ɆȽɍ. ɉɪɢ ɷɬɨɦ ɚɜɬɨɪɵ ɫɬɪɟɦɢɥɢɫɶ ɢɫɩɨɥɶɡɨɜɚɬɶ ɜ ɩɟɪɜɭɸ ɨɱɟɪɟɞɶ ɧɚɢɛɨɥɟɟ ɯɚɪɚɤɬɟɪɧɵɟ ɢ ɬɢɩɢɱɧɵɟ ɡɚɞɚɱɢ. ɋ ɷɬɨɣ ɰɟɥɶɸ ɧɚɪɹɞɭ ɫ ɨɪɢɝɢɧɚɥɶɧɵɦɢ ɡɚɞɚɱɚɦɢ ɛɵɥɢ ɢɫɩɨɥɶɡɨɜɚɧɵ ɮɨɪɦɭɥɢɪɨɜɤɢ ɭɫɥɨɜɢɣ ɡɚɞɚɱ ɢɡ ɫɭɳɟɫɬɜɭɸɳɢɯ ɭɱɟɛɧɢɤɨɜ, ɡɚɞɚɱɧɢɤɨɜ ɢ ɭɱɟɛɧɵɯ ɩɨɫɨɛɢɣ, ɤɨɬɨɪɵɟ ɩɨɞɜɟɪɝɚɥɢɫɶ ɫɭɳɟɫɬɜɟɧɧɨɦɭ ɢɫɩɪɚɜɥɟɧɢɸ ɢ ɞɨɪɚɛɨɬɤɟ.
ɉɨɫɨɛɢɟ ɪɚɡɛɢɬɨ ɩɨ ɝɥɚɜɚɦ, ɤɚɠɞɚɹ ɢɡ ɤɨɬɨɪɵɯ ɜɤɥɸɱɚɟɬ ɜ ɫɟɛɹ ɬɟɨɪɟɬɢɱɟɫɤɢɣ ɦɚɬɟɪɢɚɥ, ɨɫɧɨɜɧɵɟ ɬɢɩɵ ɡɚɞɚɱ ɢ ɦɟɬɨɞɵ ɢɯ ɪɟɲɟɧɢɹ, ɩɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ, ɚ ɬɚɤɠɟ ɡɚɞɚɱɢ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɪɟɲɟɧɢɹ.
ɇɚɫɬɨɹɳɟɟ ɩɨɫɨɛɢɟ ɩɪɟɞɧɚɡɧɚɱɟɧɨ ɞɥɹ ɫɬɭɞɟɧɬɨɜ ɜɵɫɲɢɯ ɭɱɟɛɧɵɯ ɡɚɜɟɞɟɧɢɣ ɢ ɢɦɟɟɬ ɰɟɥɶɸ ɩɨɦɨɱɶ ɢɦ ɨɜɥɚɞɟɬɶ ɨɫɧɨɜɧɵɦɢ ɦɟɬɨɞɚɦɢ ɢ ɩɪɢɨɛɪɟɫɬɢ ɧɚɜɵɤɢ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ɦɟɯɚɧɢɤɢ.
Ɋɟɰɟɧɡɟɧɬɵ: ɞ.ɮ.-ɦ. ɧ., ɩɪɨɮɟɫɫɨɪ Ƚ.ɋ. ɉɥɨɬɧɢɤɨɜ, ɞ.ɮ.-ɦ. ɧ., ɩɪɨɮɟɫɫɨɪ Ⱥ.ɋ. ɂɥɸɲɢɧ
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Ʉ ɱɢɬɚɬɟɥɹɦ ɫɟɪɢɢ ɩɨɫɨɛɢɣ «ɍɇɂȼȿɊɋɂɌȿɌɋɄɂɃ ɄɍɊɋ ɈȻɓȿɃ ɎɂɁɂɄɂ»
ɇɚ ɤɚɮɟɞɪɟ ɨɛɳɟɣ ɮɢɡɢɤɢ ɮɢɡɢɱɟɫɤɨɝɨ ɮɚɤɭɥɶɬɟɬɚ ɆȽɍ ɢɦ. Ɇ.ȼ. Ʌɨɦɨɧɨɫɨɜɚ ɫɨɡɞɚɧ ɢ ɝɨɬɨɜɢɬɫɹ ɤ ɢɡɞɚɧɢɸ «ɍɧɢɜɟɪɫɢɬɟɬɫɤɢɣ ɤɭɪɫ ɨɛɳɟɣ ɮɢɡɢɤɢ», ɩɪɟɞɧɚɡɧɚɱɟɧɧɵɣ ɞɥɹ ɫɬɭɞɟɧɬɨɜ ɮɢɡɢɱɟɫɤɢɯ ɫɩɟɰɢɚɥɶɧɨɫɬɟɣ ɜɭɡɨɜ.
Ʉɭɪɫ ɨɯɜɚɬɵɜɚɟɬ ɱɟɬɵɪɟ ɪɚɡɞɟɥɚ: «Ɇɟɯɚɧɢɤɚ», «Ɇɨɥɟɤɭɥɹɪɧɚɹ ɮɢɡɢɤɚ», «ɗɥɟɤɬɪɨɦɚɝɧɟɬɢɡɦ» ɢ «Ɉɩɬɢɤɚ». Ɉɬɥɢɱɢɬɟɥɶɧɨɣ ɨɫɨɛɟɧɧɨɫɬɶɸ ɞɚɧɧɨɝɨ ɤɭɪɫɚ ɹɜɥɹɟɬɫɹ ɬɨ, ɱɬɨ ɜ ɧɟɦ ɜ ɦɟɬɨɞɢɱɟɫɤɨɦ ɨɬɧɨɲɟɧɢɢ ɨɫɭɳɟɫɬɜɥɟɧɨ ɟɞɢɧɫɬɜɨ ɨɫɧɨɜɧɵɯ ɮɨɪɦ ɨɛɭɱɟɧɢɹ ɮɢɡɢɤɟ: ɥɟɤɰɢɢ, ɥɚɛɨɪɚɬɨɪɧɵɟ ɪɚɛɨɬɵ ɢ ɫɟɦɢɧɚɪɵ. ȼ ɫɢɫɬɟɦɟ ɭɧɢɜɟɪɫɢɬɟɬɫɤɨɝɨ ɨɛɪɚɡɨɜɚɧɢɹ ɬɟɨɪɟɬɢɱɟɫɤɢɣ ɦɚɬɟɪɢɚɥ ɢɡɥɚɝɚɟɬɫɹ ɜ ɨɫɧɨɜɧɨɦ ɜ ɥɟɤɰɢɨɧɧɵɯ ɤɭɪɫɚɯ, ɚ ɭɦɟɧɢɟ ɪɟɲɚɬɶ ɡɚɞɚɱɢ ɨɬɪɚɛɚɬɵɜɚɟɬɫɹ ɧɚ ɫɟɦɢɧɚɪɫɤɢɯ ɡɚɧɹɬɢɹɯ. Ɋɚɡɜɢɬɢɟ ɧɚɜɵɤɨɜ ɷɤɫɩɟɪɢɦɟɧɬɚ ɢ ɚɧɚɥɢɡɚ ɟɝɨ ɪɟɡɭɥɶɬɚɬɨɜ ɩɪɨɢɫɯɨɞɢɬ ɜ ɩɪɨɰɟɫɫɟ ɡɚɧɹɬɢɣ ɜ ɨɛɳɟɦ ɮɢɡɢɱɟɫɤɨɦ ɩɪɚɤɬɢɤɭɦɟ. ȼ ɫɜɹɡɢ ɫ ɷɬɢɦ, ɤɚɠɞɵɣ ɪɚɡɞɟɥ ɤɭɪɫɚ ɫɨɫɬɨɢɬ ɢɡ ɱɟɬɵɪɟɯ ɩɨɫɨɛɢɣ: «Ʌɟɤɰɢɢ», «Ʌɟɤɰɢɨɧɧɵɣ ɷɤɫɩɟɪɢɦɟɧɬ», «Ʌɚɛɨɪɚɬɨɪɧɵɣ ɩɪɚɤɬɢɤɭɦ» ɢ «Ɇɟɬɨɞɢɤɚ ɪɟɲɟɧɢɹ ɡɚɞɚɱ».
Ʉɚɠɞɚɹ ɝɥɚɜɚ ɩɨɫɨɛɢɹ «Ʌɟɤɰɢɢ» ɫɨɞɟɪɠɢɬ ɦɚɬɟɪɢɚɥ ɛɚɡɨɜɨɝɨ ɭɪɨɜɧɹ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɝɨ ɩɪɨɝɪɚɦɦɟ ɤɭɪɫɚ, ɢ ɨɬɪɚɠɚɟɬ ɫɨɜɪɟɦɟɧɧɵɟ ɬɟɧɞɟɧɰɢɢ ɢ ɬɟɯɧɨɥɨɝɢɢ ɮɢɡɢɱɟɫɤɨɝɨ ɨɛɪɚɡɨɜɚɧɢɹ. Ʌɟɤɰɢɢ ɩɨ ɤɚɠɞɨɣ ɬɟɦɟ ɫɨɩɪɨɜɨɠɞɚɸɬɫɹ ɞɟɦɨɧɫɬɪɚɰɢɟɣ ɨɫɧɨɜɧɵɯ ɮɢɡɢɱɟɫɤɢɯ ɷɤɫɩɟɪɢɦɟɧɬɨɜ, ɨɩɢɫɚɧɢɟ ɤɨɬɨɪɵɯ ɩɪɟɞɫɬɚɜɥɟɧɨ ɜ ɩɨɫɨɛɢɢ «Ʌɟɤɰɢɨɧɧɵɣ ɷɤɫɩɟɪɢɦɟɧɬ».
ɉɨɫɨɛɢɟɦ, ɩɨɡɜɨɥɹɸɳɢɦ ɪɚɡɜɢɜɚɬɶ ɭɦɟɧɢɟ ɪɟɲɚɬɶ ɮɢɡɢɱɟɫɤɢɟ ɡɚɞɚɱɢ, ɹɜɥɹɟɬɫɹ «Ɇɟɬɨɞɢɤɚ ɪɟɲɟɧɢɹ ɡɚɞɚɱ», ɤɨɬɨɪɨɟ ɫɨɫɬɚɜɥɟɧɨ ɫ ɬɚɤɢɦ ɪɚɫɱɟɬɨɦ, ɱɬɨɛɵ ɢɦ ɦɨɠɧɨ ɛɵɥɨ ɩɨɥɶɡɨɜɚɬɶɫɹ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɣ ɪɚɛɨɬɵ. ȼɟɫɶ ɦɚɬɟɪɢɚɥ ɪɚɡɛɢɬ ɧɚ ɝɥɚɜɵ. Ɋɚɡɛɨɪ ɡɚɞɚɱ ɜɫɟɯ ɝɥɚɜ ɩɪɨɜɨɞɢɬɫɹ ɩɨ ɟɞɢɧɨɣ ɫɯɟɦɟ, ɩɪɢɱɟɦ ɤɚɠɞɭɸ ɝɥɚɜɭ ɦɨɠɧɨ ɩɪɨɪɚɛɚɬɵɜɚɬɶ ɧɟɡɚɜɢɫɢɦɨ ɨɬ ɞɪɭɝɢɯ.
ɇɟɨɬɴɟɦɥɟɦɨɣ ɱɚɫɬɶɸ ɤɭɪɫɚ ɨɛɳɟɣ ɮɢɡɢɤɢ ɫɥɭɠɢɬ ɥɚɛɨɪɚɬɨɪɧɵɣ ɩɪɚɤɬɢɤɭɦ. Ɇɚɬɟɪɢɚɥɵ ɩɨɫɨɛɢɹ «Ʌɚɛɨɪɚɬɨɪɧɵɣ ɩɪɚɤɬɢɤɭɦ» ɞɨɫɬɚɬɨɱɧɵ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɣ ɩɨɞɝɨɬɨɜɤɢ ɤ ɜɵɩɨɥɧɟɧɢɸ ɪɚɛɨɬ. ȼ ɫɜɹɡɢ ɫ ɷɬɢɦ ɜ ɩɨɫɨɛɢɢ ɢɦɟɟɬɫɹ ɤɚɤ ɨɛɳɟɟ ɬɟɨɪɟɬɢɱɟɫɤɨɟ ɜɜɟɞɟɧɢɟ, ɬɚɤ ɢ ɛɨɥɟɟ ɩɨɞɪɨɛɧɨɟ ɢɡɥɨɠɟɧɢɟ ɬɟɨɪɢɢ ɤ ɤɚɠɞɨɣ ɥɚɛɨɪɚɬɨɪɧɨɣ ɪɚɛɨɬɟ. Ʉɪɨɦɟ ɬɨɝɨ, ɜ ɤɚɠɞɨɣ ɪɚɛɨɬɟ ɫɮɨɪɦɭɥɢɪɨɜɚɧɵ ɰɟɥɶ ɢ ɢɞɟɹ ɷɤɫɩɟɪɢɦɟɧɬɚ, ɞɚɧɨ ɨɩɢɫɚɧɢɟ ɭɫɬɚɧɨɜɤɢ ɢ ɩɨɞɪɨɛɧɨɟ ɢɡɥɨɠɟɧɢɟ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɩɪɨɜɟɞɟɧɢɹ ɷɤɫɩɟɪɢɦɟɧɬɚ ɢ ɨɛɪɚɛɨɬɤɢ ɪɟɡɭɥɶɬɚɬɨɜ.
ȼɫɟ ɩɨɠɟɥɚɧɢɹ ɢ ɡɚɦɟɱɚɧɢɹ ɩɨ ɩɨɫɨɛɢɹɦ ɤɭɪɫɚ ɛɭɞɭɬ ɫ ɛɥɚɝɨɞɚɪɧɨɫɬɶɸ ɩɪɢɧɹɬɵ ɢ ɪɚɫɫɦɨɬɪɟɧɵ ɧɚ ɤɚɮɟɞɪɟ ɨɛɳɟɣ ɮɢɡɢɤɢ ɮɢɡɢɱɟɫɤɨɝɨ ɮɚɤɭɥɶɬɟɬɚ ɆȽɍ ɢɦ. Ɇ.ȼ. Ʌɨɦɨɧɨɫɨɜɚ.
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ɉɪɟɞɢɫɥɨɜɢɟ ................................................................................................... |
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Ƚɥɚɜɚ 1. Ʉɢɧɟɦɚɬɢɤɚ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ ɢ ɩɪɨɫɬɟɣɲɢɯ |
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ɫɢɫɬɟɦ ................................................................................................ |
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1.1. Ɍɟɨɪɟɬɢɱɟɫɤɢɣ ɦɚɬɟɪɢɚɥ ................................................................. |
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1.2. Ɉɫɧɨɜɧɵɟ ɬɢɩɵ ɡɚɞɚɱ ɢ ɦɟɬɨɞɵ ɢɯ ɪɟɲɟɧɢɹ ............................... |
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1.2.1. Ʉɥɚɫɫɢɮɢɤɚɰɢɹ ɡɚɞɚɱ ɤɢɧɟɦɚɬɢɤɢ ...................................... |
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1.2.2. Ɉɛɳɚɹ ɫɯɟɦɚ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ɤɢɧɟɦɚɬɢɤɢ ........................... |
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1.3. ɉɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ............................................................... |
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1.4. Ɂɚɞɚɱɢ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɪɟɲɟɧɢɹ......................................... |
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Ƚɥɚɜɚ 2. Ⱦɢɧɚɦɢɤɚ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ ɢ ɩɪɨɫɬɟɣɲɢɯ |
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ɫɢɫɬɟɦ .............................................................................................. |
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2.1. Ɍɟɨɪɟɬɢɱɟɫɤɢɣ ɦɚɬɟɪɢɚɥ ............................................................... |
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2.1.1. Ɂɚɤɨɧɵ ɇɶɸɬɨɧɚ ................................................................... |
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2.1.2. Ɂɚɤɨɧɵ, ɨɩɢɫɵɜɚɸɳɢɟ ɢɧɞɢɜɢɞɭɚɥɶɧɵɟ ɫɜɨɣɫɬɜɚ ɫɢɥ ..... |
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2.2. Ɉɫɧɨɜɧɵɟ ɬɢɩɵ ɡɚɞɚɱ ɢ ɦɟɬɨɞɵ ɢɯ ɪɟɲɟɧɢɹ ............................... |
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2.2.1. Ʉɥɚɫɫɢɮɢɤɚɰɢɹ ɡɚɞɚɱ ɞɢɧɚɦɢɤɢ .......................................... |
51 |
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2.2.2. Ɉɛɳɚɹ ɫɯɟɦɚ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ɞɢɧɚɦɢɤɢ ɫ ɩɨɦɨɳɶɸ |
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ɡɚɤɨɧɨɜ ɇɶɸɬɨɧɚ .................................................................. |
51 |
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2.3. ɉɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ................................................................ |
52 |
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2.4. Ɂɚɞɚɱɢ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɪɟɲɟɧɢɹ ........................................ |
75 |
Ƚɥɚɜɚ 3. Ɂɚɤɨɧɵ ɢɡɦɟɧɟɧɢɹ ɢɦɩɭɥɶɫɚ ɢ ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ |
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ɫɢɫɬɟɦɵ ɦɚɬɟɪɢɚɥɶɧɵɯ ɬɨɱɟɤ..................................................... |
80 |
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3.1. Ɍɟɨɪɟɬɢɱɟɫɤɢɣ ɦɚɬɟɪɢɚɥ . .............................................................. |
80 |
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3.1.1. ɂɦɩɭɥɶɫ ɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ......................................... |
80 |
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3.1.2. Ɋɚɛɨɬɚ ɫɢɥ .............................................................................. |
83 |
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3.1.3. ɗɧɟɪɝɢɹ ɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ........................................... |
87 |
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3.1.4. ɋɬɨɥɤɧɨɜɟɧɢɟ ɬɟɥ ................................................................. |
89 |
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3.2. Ɉɫɧɨɜɧɵɟ ɬɢɩɵ ɡɚɞɚɱ ɢ ɦɟɬɨɞɵ ɢɯ ɪɟɲɟɧɢɹ ............................... |
89 |
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3.2.1. Ʉɥɚɫɫɢɮɢɤɚɰɢɹ ɡɚɞɚɱ ........................................................... |
89 |
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3.2.2. Ɉɛɳɚɹ ɫɯɟɦɚ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ................................................ |
90 |
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3.3. ɉɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ............................................................... |
91 |
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3.4. Ɂɚɞɚɱɢ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɪɟɲɟɧɢɹ ...................................... |
112 |
Ƚɥɚɜɚ 4. Ⱦɜɢɠɟɧɢɟ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ ɜ ɧɟɢɧɟɪɰɢɚɥɶɧɵɯ |
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ɫɢɫɬɟɦɚɯ ɨɬɫɱɟɬɚ. ɋɢɥɵ ɢɧɟɪɰɢɢ ............................................ |
116 |
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4.1. Ɍɟɨɪɟɬɢɱɟɫɤɢɣ ɦɚɬɟɪɢɚɥ ............................................................. |
116 |
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4.2. Ɉɫɧɨɜɧɵɟ ɬɢɩɵ ɡɚɞɚɱ ɢ ɦɟɬɨɞɵ ɢɯ ɪɟɲɟɧɢɹ ............................. |
119 |
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4.2.1. Ʉɥɚɫɫɢɮɢɤɚɰɢɹ ɡɚɞɚɱ ......................................................... |
119 |
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4.2.2. Ɉɛɳɚɹ ɫɯɟɦɚ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ɦɟɯɚɧɢɤɢ ɜ ɧɟɢɧɟɪɰɢɚɥɶɧɵɯ |
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ɫɢɫɬɟɦɚɯ ɨɬɫɱɟɬɚ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɡɚɤɨɧɨɜ ɇɶɸɬɨɧɚ .... |
120 |
Ɉɝɥɚɜɥɟɧɢɟ |
5 |
4.3. ɉɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ............................................................. |
121 |
4.4. Ɂɚɞɚɱɢ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɪɟɲɟɧɢɹ ...................................... |
142 |
Ƚɥɚɜɚ 5. Ʉɢɧɟɦɚɬɢɤɚ ɜ ɬɟɨɪɢɢ ɨɬɧɨɫɢɬɟɥɶɧɨɫɬɢ ................................. |
146 |
5.1. Ɍɟɨɪɟɬɢɱɟɫɤɢɣ ɦɚɬɟɪɢɚɥ ............................................................. |
146 |
5.1.1. ɉɨɫɬɭɥɚɬɵ ɢ ɨɫɧɨɜɧɵɟ ɩɨɧɹɬɢɹ (ɫɩɟɰɢɚɥɶɧɨɣ) ɬɟɨɪɢɢ |
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ɨɬɧɨɫɢɬɟɥɶɧɨɫɬɢ .................................................................. |
146 |
5.1.2. ɉɪɟɨɛɪɚɡɨɜɚɧɢɹ Ʌɨɪɟɧɰɚ ................................................... |
147 |
5.1.3. ɋɥɟɞɫɬɜɢɹ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ Ʌɨɪɟɧɰɚ ................................. |
149 |
5.1.4. ɉɪɨɫɬɪɚɧɫɬɜɟɧɧɨ-ɜɪɟɦɟɧɧɨɣ ɢɧɬɟɪɜɚɥ ............................ |
151 |
5.1.5. ɉɪɟɨɛɪɚɡɨɜɚɧɢɟ (ɫɥɨɠɟɧɢɟ) ɫɤɨɪɨɫɬɟɣ ............................ |
154 |
5.2. Ɉɫɧɨɜɧɵɟ ɬɢɩɵ ɡɚɞɚɱ ɢ ɦɟɬɨɞɵ ɢɯ ɪɟɲɟɧɢɹ ............................. |
155 |
5.2.1. Ʉɥɚɫɫɢɮɢɤɚɰɢɹ ɡɚɞɚɱ ɤɢɧɟɦɚɬɢɤɢ ɜ ɬɟɨɪɢɢ ɨɬɧɨɫɢɬɟɥɶ- |
|
ɧɨɫɬɢ ..................................................................................... |
155 |
5.2.2. Ɉɛɳɚɹ ɫɯɟɦɚ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ɤɢɧɟɦɚɬɢɤɢ ɜ ɬɟɨɪɢɢ |
|
ɨɬɧɨɫɢɬɟɥɶɧɨɫɬɢ .................................................................. |
156 |
5.3. ɉɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ............................................................. |
157 |
5.4. Ɂɚɞɚɱɢ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɪɟɲɟɧɢɹ ...................................... |
180 |
Ƚɥɚɜɚ 6. Ʉɢɧɟɦɚɬɢɤɚ ɢ ɞɢɧɚɦɢɤɚ ɚɛɫɨɥɸɬɧɨ ɬɜɟɪɞɨɝɨ ɬɟɥɚ ............. |
184 |
6.1. Ɍɟɨɪɟɬɢɱɟɫɤɢɣ ɦɚɬɟɪɢɚɥ ............................................................. |
184 |
6.1.1. Ʉɢɧɟɦɚɬɢɤɚ ɚɛɫɨɥɸɬɧɨ ɬɜɟɪɞɨɝɨ ɬɟɥɚ .............................. |
184 |
6.1.2. Ⱦɢɧɚɦɢɤɚ ɚɛɫɨɥɸɬɧɨ ɬɜɟɪɞɨɝɨ ɬɟɥɚ ................................. |
190 |
6.2. Ɉɫɧɨɜɧɵɟ ɬɢɩɵ ɡɚɞɚɱ ɢ ɦɟɬɨɞɵ ɢɯ ɪɟɲɟɧɢɹ.............................. |
198 |
6.2.1. Ʉɥɚɫɫɢɮɢɤɚɰɢɹ ɡɚɞɚɱ ɤɢɧɟɦɚɬɢɤɢ ɢ ɞɢɧɚɦɢɤɢ ɚɛɫɨɥɸɬ- |
|
ɧɨ ɬɜɟɪɞɨɝɨ ɬɟɥɚ .................................................................. |
198 |
6.2.2. Ɉɛɳɚɹ ɫɯɟɦɚ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ɤɢɧɟɦɚɬɢɤɢ ɢ ɞɢɧɚɦɢɤɢ |
|
ɚɛɫɨɥɸɬɧɨ ɬɜɟɪɞɨɝɨ ɬɟɥɚ .................................................... |
199 |
6.3. ɉɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ............................................................. |
200 |
6.3.1. Ʉɢɧɟɦɚɬɢɤɚ ɚɛɫɨɥɸɬɧɨ ɬɜɟɪɞɨɝɨ ɬɟɥɚ .............................. |
200 |
6.3.2. Ⱦɢɧɚɦɢɤɚ ɚɛɫɨɥɸɬɧɨ ɬɜɟɪɞɨɝɨ ɬɟɥɚ ................................. |
208 |
6.4. Ɂɚɞɚɱɢ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɪɟɲɟɧɢɹ ...................................... |
226 |
Ƚɥɚɜɚ 7. Ɂɚɤɨɧɵ ɫɨɯɪɚɧɟɧɢɹ ɦɨɦɟɧɬɚ ɢɦɩɭɥɶɫɚ ɢ ɷɧɟɪɝɢɢ. |
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Ƚɢɪɨɫɤɨɩɵ. Ƚɢɪɨɫɤɨɩɢɱɟɫɤɢɟ ɫɢɥɵ . ...................................... |
231 |
7.1. Ɍɟɨɪɟɬɢɱɟɫɤɢɣ ɦɚɬɟɪɢɚɥ ............................................................. |
231 |
7.2. Ɉɫɧɨɜɧɵɟ ɬɢɩɵ ɡɚɞɚɱ ɢ ɦɟɬɨɞɵ ɢɯ ɪɟɲɟɧɢɹ ............................. |
237 |
7.2.1. Ʉɥɚɫɫɢɮɢɤɚɰɢɹ ɡɚɞɚɱ ......................................................... |
237 |
7.2.2. Ɉɛɳɚɹ ɫɯɟɦɚ ɪɟɲɟɧɢɹ ɡɚɞɚɱ .............................................. |
237 |
7.3. ɉɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ............................................................. |
238 |
7.3.1. Ɂɚɤɨɧɵ ɫɨɯɪɚɧɟɧɢɹ ɢɦɩɭɥɶɫɚ ɢ ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ .. |
238 |
7.3.2. Ƚɢɪɨɫɤɨɩɵ. Ƚɢɪɨɫɤɨɩɢɱɟɫɤɢɟ ɫɢɥɵ .................................. |
258 |
7.4. Ɂɚɞɚɱɢ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɪɟɲɟɧɢɹ ...................................... |
266 |
6 |
Ɉɝɥɚɜɥɟɧɢɟ |
Ƚɥɚɜɚ 8. ɋɜɨɛɨɞɧɵɟ ɢ ɜɵɧɭɠɞɟɧɧɵɟ ɤɨɥɟɛɚɧɢɹ ɫɢɫɬɟɦ ɫ ɨɞɧɨɣ |
|
ɫɬɟɩɟɧɶɸ ɫɜɨɛɨɞɵ. Ɋɟɡɨɧɚɧɫ ..................................................... |
270 |
8.1. Ɍɟɨɪɟɬɢɱɟɫɤɢɣ ɦɚɬɟɪɢɚɥ . ............................................................ |
270 |
8.1.1. ɋɨɛɫɬɜɟɧɧɵɟ ɝɚɪɦɨɧɢɱɟɫɤɢɟ ɤɨɥɟɛɚɧɢɹ .......................... |
271 |
8.1.2. ɋɨɛɫɬɜɟɧɧɵɟ ɡɚɬɭɯɚɸɳɢɟ ɤɨɥɟɛɚɧɢɹ ............................... |
277 |
8.1.3. ȼɵɧɭɠɞɟɧɧɵɟ ɤɨɥɟɛɚɧɢɹ. Ɋɟɡɨɧɚɧɫ ................................. |
281 |
8.2. Ɉɫɧɨɜɧɵɟ ɬɢɩɵ ɡɚɞɚɱ ɢ ɦɟɬɨɞɵ ɢɯ ɪɟɲɟɧɢɹ ............................. |
284 |
8.2.1. Ʉɥɚɫɫɢɮɢɤɚɰɢɹ ɡɚɞɚɱ ......................................................... |
284 |
8.2.2. Ɉɛɳɚɹ ɫɯɟɦɚ ɪɟɲɟɧɢɹ ɡɚɞɚɱ .............................................. |
285 |
8.3. ɉɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ............................................................. |
285 |
8.4. Ɂɚɞɚɱɢ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɪɟɲɟɧɢɹ ...................................... |
322 |
Ƚɥɚɜɚ 9. Ȼɟɝɭɳɢɟ ɢ ɫɬɨɹɱɢɟ ɜɨɥɧɵ. Ɇɨɞɵ ɢ ɧɨɪɦɚɥɶɧɵɟ ɱɚɫɬɨɬɵ . 326
9.1. Ɍɟɨɪɟɬɢɱɟɫɤɢɣ ɦɚɬɟɪɢɚɥ ............................................................. |
326 |
9.1.1. ȼɨɥɧɨɜɨɟ ɭɪɚɜɧɟɧɢɟ ........................................................... |
326 |
9.1.2. ɉɥɨɫɤɢɟ ɜɨɥɧɵ .................................................................... |
327 |
9.1.3. ɋɮɟɪɢɱɟɫɤɢɟ ɜɨɥɧɵ ............................................................ |
329 |
9.1.4. ɋɤɨɪɨɫɬɢ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɭɩɪɭɝɢɯ ɜɨɥɧ ɜ ɪɚɡɥɢɱɧɵɯ |
|
ɫɪɟɞɚɯ ................................................................................... |
331 |
9.1.5. ɗɧɟɪɝɟɬɢɱɟɫɤɢɟ ɫɨɨɬɧɨɲɟɧɢɹ ........................................... |
336 |
9.1.6. ɉɪɨɞɨɥɶɧɵɣ ɷɮɮɟɤɬ Ⱦɨɩɥɟɪɚ (ɤɥɚɫɫɢɱɟɫɤɢɣ) ................. |
338 |
9.1.7. ɋɨɛɫɬɜɟɧɧɵɟ ɤɨɥɟɛɚɧɢɹ ɪɚɫɩɪɟɞɟɥɟɧɧɵɯ ɫɢɫɬɟɦ ........... |
339 |
9.2. Ɉɫɧɨɜɧɵɟ ɬɢɩɵ ɡɚɞɚɱ ɢ ɦɟɬɨɞɵ ɢɯ ɪɟɲɟɧɢɹ ............................. |
344 |
9.2.1. Ʉɥɚɫɫɢɮɢɤɚɰɢɹ ɡɚɞɚɱ ......................................................... |
344 |
9.2.2. Ɉɛɳɚɹ ɫɯɟɦɚ ɪɟɲɟɧɢɹ ɡɚɞɚɱ .............................................. |
345 |
9.3. ɉɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ............................................................. |
346 |
9.4. Ɂɚɞɚɱɢ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɪɟɲɟɧɢɹ ...................................... |
362 |
Ʌɢɬɟɪɚɬɭɪɚ ................................................................................................. |
365 |
ɉɪɟɞɢɫɥɨɜɢɟ |
7 |
ɉɊȿȾɂɋɅɈȼɂȿ
Ɇɟɬɨɞɢɱɟɫɤɨɟ ɩɨɫɨɛɢɟ ɩɨ ɪɟɲɟɧɢɸ ɡɚɞɚɱ ɦɟɯɚɧɢɤɢ ɩɪɟɞɧɚɡɧɚɱɚɟɬɫɹ ɞɥɹ ɫɬɭɞɟɧɬɨɜ ɮɢɡɢɱɟɫɤɢɯ ɫɩɟɰɢɚɥɶɧɨɫɬɟɣ ɜɵɫɲɢɯ ɭɱɟɛɧɵɯ ɡɚɜɟɞɟɧɢɣ ɢ ɧɚɩɢɫɚɧɨ ɧɚ ɨɫɧɨɜɟ ɦɧɨɝɨɥɟɬɧɟɝɨ ɨɩɵɬɚ ɩɪɨɜɟɞɟɧɢɹ ɚɜɬɨɪɚɦɢ ɡɚɧɹɬɢɣ ɩɨ ɨɛɳɟɣ ɮɢɡɢɤɟ ɫɨ ɫɬɭɞɟɧɬɚɦɢ ɮɢɡɢɱɟɫɤɨɝɨ ɮɚɤɭɥɶɬɟɬɚ Ɇɨɫɤɨɜɫɤɨɝɨ ɝɨɫɭɞɚɪɫɬɜɟɧɧɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ ɢɦ. Ɇ. ȼ. Ʌɨɦɨɧɨɫɨɜɚ.
Ɉɩɵɬ ɩɪɨɜɟɞɟɧɢɹ ɡɚɧɹɬɢɣ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɜ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ, ɤ ɫɨɠɚɥɟɧɢɸ, ɧɚɛɥɸɞɚɟɬɫɹ ɡɚɦɟɬɧɨɟ ɫɧɢɠɟɧɢɟ ɫɪɟɞɧɟɝɨ ɭɪɨɜɧɹ ɩɨɞɝɨɬɨɜɤɢ ɜɵɩɭɫɤɧɢɤɨɜ ɫɪɟɞɧɢɯ ɭɱɟɛɧɵɯ ɡɚɜɟɞɟɧɢɣ ɜ ɨɛɥɚɫɬɢ ɮɢɡɢɤɢ ɩɪɢ ɫɨɯɪɚɧɟɧɢɢ ɜɵɫɨɤɨɝɨ ɭɪɨɜɧɹ ɭ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɟɛɨɥɶɲɨɣ ɱɚɫɬɢ ɜɱɟɪɚɲɧɢɯ ɲɤɨɥɶɧɢɤɨɜ. ɉɪɟɩɨɞɚɜɚɬɟɥɢ ɜɵɧɭɠɞɟɧɵ ɨɪɢɟɧɬɢɪɨɜɚɬɶɫɹ ɧɚ ɫɪɟɞɧɟɝɨ ɫɬɭɞɟɧɬɚ, ɢ ɧɟ ɢɦɟɸɬ ɜɨɡɦɨɠɧɨɫɬɢ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɧɚ ɫɟɦɢɧɚɪɚɯ ɡɚɞɚɱɢ ɩɨɜɵɲɟɧɧɨɣ ɫɥɨɠɧɨɫɬɢ. ɉɨɷɬɨɦɭ ɜɨɡɪɚɫɬɚɟɬ ɪɨɥɶ ɦɟɬɨɞɢɱɟɫɤɢɯ ɩɨɫɨɛɢɣ, ɨɪɢɟɧɬɢɪɨɜɚɧɧɵɯ ɧɚ ɫɚɦɨɫɬɨɹɬɟɥɶɧɭɸ ɪɚɛɨɬɭ ɫɬɭɞɟɧɬɨɜ.
ɇɚɦɢ ɧɚɩɢɫɚɧɨ ɦɟɬɨɞɢɱɟɫɤɨɟ ɩɨɫɨɛɢɟ ɩɨ ɪɟɲɟɧɢɸ ɡɚɞɚɱ ɦɟɯɚɧɢɤɢ ɞɥɹ ɫɬɭɞɟɧɬɨɜ ɩɟɪɜɨɝɨ ɤɭɪɫɚ, ɜ ɤɨɬɨɪɨɦ ɢɡɥɨɠɟɧɵ ɨɫɧɨɜɧɵɟ ɦɟɬɨɞɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ɪɚɡɥɢɱɧɵɯ ɬɢɩɨɜ ɢ ɩɪɢɜɟɞɟɧɵ ɨɫɧɨɜɧɵɟ ɬɟɨɪɟɬɢɱɟɫɤɢɟ ɫɜɟɞɟɧɢɹ ɩɨ ɤɚɠɞɨɣ ɬɟɦɟ, ɧɟɨɛɯɨɞɢɦɵɟ ɩɪɢ ɪɟɲɟɧɢɢ ɡɚɞɚɱ. ɐɟɥɶɸ ɞɚɧɧɨɝɨ ɩɨɫɨɛɢɹ ɹɜɥɹɟɬɫɹ:
1)ɩɨɦɨɱɶ ɫɬɭɞɟɧɬɚɦ ɨɜɥɚɞɟɬɶ ɨɫɧɨɜɧɵɦɢ ɦɟɬɨɞɚɦɢ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ɦɟɯɚɧɢɤɢ;
2)ɞɚɬɶ ɜɨɡɦɨɠɧɨɫɬɶ ɫɢɥɶɧɵɦ ɫɬɭɞɟɧɬɚɦ ɧɟ ɨɝɪɚɧɢɱɢɜɚɬɶɫɹ ɡɚɞɚɱɚɦɢ ɫɪɟɞɧɟɝɨ ɭɪɨɜɧɹ, ɪɚɡɛɢɪɚɟɦɵɦɢ ɧɚ ɫɟɦɢɧɚɪɫɤɢɯ ɡɚɧɹɬɢɹɯ, ɚ ɨɡɧɚɤɨɦɢɬɶɫɹ ɫ ɪɟɲɟɧɢɟɦ ɡɚɞɚɱ ɩɨɜɵɲɟɧɧɨɣ ɫɥɨɠɧɨɫɬɢ.
ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ ɫɨɫɬɨɢɬ ɢɡ ɨɝɥɚɜɥɟɧɢɹ, ɞɟɜɹɬɢ ɝɥɚɜ ɢ ɫɩɢɫɤɚ ɥɢɬɟɪɚɬɭɪɵ. Ɋɚɡɛɢɟɧɢɟ ɧɚ ɝɥɚɜɵ ɩɪɨɜɟɞɟɧɨ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɬɟɦɚɦɢ ɫɟɦɢɧɚɪɫɤɢɯ ɡɚɧɹɬɢɣ ɫɨ ɫɬɭɞɟɧɬɚɦɢ ɩɟɪɜɨɝɨ ɤɭɪɫɚ ɮɢɡɢɱɟɫɤɨɝɨ ɮɚɤɭɥɶɬɟɬɚ ɆȽɍ.
ɋɬɪɭɤɬɭɪɚ ɢɡɥɨɠɟɧɢɹ ɜɫɟɯ ɬɟɦ ɨɞɢɧɚɤɨɜɚ, ɩɪɢɱɟɦ ɤɚɠɞɚɹ ɝɥɚɜɚ ɜɤɥɸɱɚɟɬ ɜ ɫɟɛɹ ɫɥɟɞɭɸɳɢɟ ɪɚɡɞɟɥɵ:
1)ɬɟɨɪɟɬɢɱɟɫɤɢɣ ɦɚɬɟɪɢɚɥ,
2)ɨɫɧɨɜɧɵɟ ɬɢɩɵ ɡɚɞɚɱ ɢ ɦɟɬɨɞɵ ɢɯ ɪɟɲɟɧɢɹ,
3)ɩɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ,
4)ɡɚɞɚɱɢ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɪɟɲɟɧɢɹ.
Ɍɟɨɪɟɬɢɱɟɫɤɢɣ ɦɚɬɟɪɢɚɥ, ɩɪɟɞɫɬɚɜɥɟɧɧɵɣ ɜ ɧɚɱɚɥɟ ɤɚɠɞɨɣ ɝɥɚɜɵ, ɫɨɞɟɪɠɢɬ ɨɫɧɨɜɧɵɟ ɨɩɪɟɞɟɥɟɧɢɹ ɮɢɡɢɱɟɫɤɢɯ ɩɨɧɹɬɢɣ ɢ ɜɟɥɢɱɢɧ, ɮɨɪɦɭɥɢɪɨɜɤɢ ɡɚɤɨɧɨɜ, ɚ ɬɚɤɠɟ ɧɟɨɛɯɨɞɢɦɵɟ ɞɥɹ ɪɟɲɟɧɢɹ
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ɆȿɏȺɇɂɄȺ. ɆȿɌɈȾɂɄȺ Ɋȿɒȿɇɂə ɁȺȾȺɑ |
ɡɚɞɚɱ ɮɨɪɦɭɥɵ. Ɉɫɧɨɜɧɵɟ ɮɢɡɢɱɟɫɤɢɟ ɩɨɧɹɬɢɹ ɜɵɞɟɥɟɧɵ ɜ ɬɟɤɫɬɟ ɠɢɪɧɵɦ ɲɪɢɮɬɨɦ. ɑɚɫɬɶ ɮɨɪɦɭɥ, ɩɪɢɜɟɞɟɧɧɵɯ ɜ Ɍɟɨɪɟɬɢɱɟɫɤɨɦ ɦɚɬɟɪɢɚɥɟ ɤɚɠɞɨɣ ɝɥɚɜɵ, ɫɨɩɪɨɜɨɠɞɚɟɬɫɹ ɤɪɚɬɤɢɦ ɜɵɜɨɞɨɦ. ɉɪɢ ɢɡɥɨɠɟɧɢɢ ɬɟɨɪɟɬɢɱɟɫɤɨɝɨ ɦɚɬɟɪɢɚɥɚ ɛɵɥɢ ɢɫɩɨɥɶɡɨɜɚɧɵ ɲɢɪɨɤɨ ɢɡɜɟɫɬɧɵɟ ɭɱɟɛɧɢɤɢ, ɭɱɟɛɧɵɟ ɩɨɫɨɛɢɹ ɢ ɫɩɪɚɜɨɱɧɚɹ ɥɢɬɟɪɚɬɭɪɚ, ɫɩɢɫɨɤ ɤɨɬɨɪɵɯ ɩɪɢɜɟɞɟɧ ɜ ɤɨɧɰɟ ɤɧɢɝɢ.
ȼ ɩɨɫɨɛɢɢ ɞɚɟɬɫɹ ɤɥɚɫɫɢɮɢɤɚɰɢɹ ɡɚɞɚɱ ɩɨ ɤɚɠɞɨɣ ɬɟɦɟ ɢ ɩɪɟɞɥɚɝɚɸɬɫɹ ɦɟɬɨɞɵ ɢɯ ɪɟɲɟɧɢɹ. ȼ ɤɚɠɞɨɣ ɝɥɚɜɟ ɩɪɢɜɟɞɟɧɨ ɩɨɞɪɨɛɧɨɟ ɪɟɲɟɧɢɟ 10 – 12 ɡɚɞɚɱ ɢ ɩɪɟɞɥɨɠɟɧɨ 10 – 12 ɡɚɞɚɱ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɪɟɲɟɧɢɹ ɫ ɨɬɜɟɬɚɦɢ. Ⱥɜɬɨɪɵ ɫɬɪɟɦɢɥɢɫɶ ɢɫɩɨɥɶɡɨɜɚɬɶ ɜ ɩɟɪɜɭɸ ɨɱɟɪɟɞɶ ɧɚɢɛɨɥɟɟ ɯɚɪɚɤɬɟɪɧɵɟ ɡɚɞɚɱɢ. ɋ ɷɬɨɣ ɰɟɥɶɸ ɧɚɪɹɞɭ ɫ ɨɪɢɝɢɧɚɥɶɧɵɦɢ ɡɚɞɚɱɚɦɢ ɛɵɥɢ ɢɫɩɨɥɶɡɨɜɚɧɵ ɮɨɪɦɭɥɢɪɨɜɤɢ ɭɫɥɨɜɢɣ ɡɚɞɚɱ ɢɡ ɫɭɳɟɫɬɜɭɸɳɢɯ ɭɱɟɛɧɢɤɨɜ, ɡɚɞɚɱɧɢɤɨɜ ɢ ɭɱɟɛɧɵɯ ɩɨɫɨɛɢɣ, ɤɨɬɨɪɵɟ ɩɨɞɜɟɪɝɚɥɢɫɶ ɫɭɳɟɫɬɜɟɧɧɨɦɭ ɢɫɩɪɚɜɥɟɧɢɸ ɢ ɤɨɪɪɟɤɰɢɢ. Ɋɟɲɟɧɢɟ ɤɚɠɞɨɣ ɡɚɞɚɱɢ ɢɡɥɚɝɚɟɬɫɹ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɩɪɟɞɥɨɠɟɧɧɨɣ ɜ Ɍɟɨɪɟɬɢɱɟɫɤɨɦ ɦɚɬɟɪɢɚɥɟ ɨɛɳɟɣ ɫɯɟɦɨɣ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ɩɨ ɞɚɧɧɨɣ ɬɟɦɟ ɢ ɫɨɩɪɨɜɨɠɞɚɟɬɫɹ ɪɢɫɭɧɤɚɦɢ ɫ ɢɡɨɛɪɚɠɟɧɢɟɦ ɤɢɧɟɦɚɬɢɱɟɫɤɢɯ ɢ ɞɢɧɚɦɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɫɢɫɬɟɦɵ ɬɟɥ.
Ɉɫɨɛɨɟ ɜɧɢɦɚɧɢɟ ɩɪɢ ɢɡɥɨɠɟɧɢɢ ɦɚɬɟɪɢɚɥɚ ɭɞɟɥɹɟɬɫɹ ɜɵɛɨɪɭ ɦɨɞɟɥɟɣ ɦɚɬɟɪɢɚɥɶɧɵɯ ɨɛɴɟɤɬɨɜ ɢ ɹɜɥɟɧɢɣ ɧɚ ɧɚɱɚɥɶɧɨɦ ɷɬɚɩɟ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ. Ɉɫɨɛɟɧɧɨɫɬɶɸ ɩɪɟɞɥɚɝɚɟɦɨɝɨ ɦɟɬɨɞɢɱɟɫɤɨɝɨ ɩɨɫɨɛɢɹ ɹɜɥɹɟɬɫɹ ɬɚɤɠɟ ɢɡɥɨɠɟɧɢɟ ɪɚɡɥɢɱɧɵɯ ɦɟɬɨɞɨɜ ɪɟɲɟɧɢɹ ɤɨɧɤɪɟɬɧɨɣ ɡɚɞɚɱɢ ɢ ɢɯ ɫɪɚɜɧɟɧɢɟ.
ɉɨɫɨɛɢɟ, ɢɡɞɚɧɧɨɟ ɩɨ ɝɥɚɜɚɦ ɧɟɛɨɥɶɲɢɦ ɬɢɪɚɠɨɦ, ɩɪɨɲɥɨ ɚɩɪɨɛɚɰɢɸ. ɉɪɟɩɨɞɚɜɚɬɟɥɢ, ɜɟɞɭɳɢɟ ɡɚɧɹɬɢɹ ɧɚ ɩɟɪɜɨɦ ɤɭɪɫɟ ɮɢɡɢɱɟɫɤɨɝɨ ɮɚɤɭɥɶɬɟɬɚ ɆȽɍ, ɜ ɬɟɱɟɧɢɟ ɬɪɟɯ ɥɟɬ ɢɫɩɨɥɶɡɨɜɚɥɢ ɟɝɨ ɩɪɢ ɩɪɨɜɟɞɟɧɢɢ ɡɚɧɹɬɢɣ ɢ ɜɵɫɤɚɡɚɥɢ ɫɜɨɢ ɡɚɦɟɱɚɧɢɹ ɢ ɩɪɟɞɥɨɠɟɧɢɹ, ɤɨɬɨɪɵɟ ɛɵɥɢ ɭɱɬɟɧɵ ɚɜɬɨɪɚɦɢ ɩɪɢ ɩɨɞɝɨɬɨɜɤɟ ɤɧɢɠɧɨɝɨ ɜɚɪɢɚɧɬɚ. Ⱥɜɬɨɪɵ ɜɵɪɚɠɚɸɬ ɝɥɭɛɨɤɭɸ ɛɥɚɝɨɞɚɪɧɨɫɬɶ ɜɫɟɦ ɩɪɟɩɨɞɚɜɚɬɟɥɹɦ ɤɚɮɟɞɪɵ ɨɛɳɟɣ ɮɢɡɢɤɢ ɮɢɡɢɱɟɫɤɨɝɨ ɮɚɤɭɥɶɬɟɬɚ ɆȽɍ ɡɚ ɩɥɨɞɨɬɜɨɪɧɵɟ ɞɢɫɤɭɫɫɢɢ ɢ ɰɟɧɧɵɟ ɡɚɦɟɱɚɧɢɹ, ɜɵɫɤɚɡɚɧɧɵɟ ɜ ɩɪɨɰɟɫɫɟ ɧɚɩɢɫɚɧɢɹ ɞɚɧɧɨɝɨ ɭɱɟɛɧɨɝɨ ɩɨɫɨɛɢɹ.
Ƚɥɚɜɚ 1. Ʉɢɧɟɦɚɬɢɤɚ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ ɢ ɩɪɨɫɬɟɣɲɢɯ ɫɢɫɬɟɦ |
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ȽɅȺȼȺ 1 ɄɂɇȿɆȺɌɂɄȺ ɆȺɌȿɊɂȺɅɖɇɈɃ ɌɈɑɄɂ ɂ
ɉɊɈɋɌȿɃɒɂɏ ɋɂɋɌȿɆ
1.1. Ɍɟɨɪɟɬɢɱɟɫɤɢɣ ɦɚɬɟɪɢɚɥ
Ɏɢɡɢɱɟɫɤɚɹ ɜɟɥɢɱɢɧɚ – ɷɬɨ ɤɨɥɢɱɟɫɬɜɟɧɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɫɜɨɣɫɬɜɚ ɦɚɬɟɪɢɚɥɶɧɵɯ ɨɛɴɟɤɬɨɜ ɢɥɢ ɹɜɥɟɧɢɣ (ɩɪɨɰɟɫɫɨɜ). Ʉɚɠɞɚɹ ɮɢɡɢɱɟɫɤɚɹ ɜɟɥɢɱɢɧɚ ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɨɞɧɨɡɧɚɱɧɵɦ ɫɩɨɫɨɛɨɦ ɟɟ ɢɡɦɟɪɟɧɢɹ – ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɝɨ ɨɩɪɟɞɟɥɟɧɢɹ ɢɥɢ ɪɚɫɱɟɬɚ. Ɉɩɪɟɞɟɥɟɧɢɟ ɮɢɡɢɱɟɫɤɨɣ ɜɟɥɢɱɢɧɵ ɭɤɚɡɵɜɚɟɬ ɩɪɢɧɰɢɩɢɚɥɶɧɵɣ ɫɩɨɫɨɛ ɟɟ ɢɡɦɟɪɟɧɢɹ.
Ɏɢɡɢɱɟɫɤɨɟ ɩɨɧɹɬɢɟ (ɦɨɞɟɥɶ ɨɛɴɟɤɬɚ ɢɥɢ ɹɜɥɟɧɢɹ) – ɷɬɨ ɚɛɫɬɪɚɤɰɢɹ (ɮɢɥɨɫ.), ɤɨɬɨɪɚɹ ɨɬɪɚɠɚɟɬ ɬɨɥɶɤɨ ɨɫɧɨɜɧɵɟ, ɧɚɢɛɨɥɟɟ ɫɭɳɟɫɬɜɟɧɧɵɟ, ɫɜɨɣɫɬɜɚ ɦɚɬɟɪɢɚɥɶɧɵɯ ɨɛɴɟɤɬɨɜ ɢɥɢ ɹɜɥɟɧɢɣ (ɩɪɨɰɟɫɫɨɜ).
Ʉɪɢɬɟɪɢɣ ɩɪɚɜɢɥɶɧɨɫɬɢ ɜɵɛɨɪɚ ɦɨɞɟɥɢ. ȿɫɥɢ ɜ ɞɚɧɧɨɣ ɡɚɞɚɱɟ ɮɢɡɢɱɟɫɤɚɹ ɜɟɥɢɱɢɧɚ, ɨɩɢɫɵɜɚɸɳɚɹ ɧɟɨɫɧɨɜɧɨɟ ɫɜɨɣɫɬɜɨ, ɨɬ ɤɨɬɨɪɨɝɨ ɦɵ ɚɛɫɬɪɚɝɢɪɭɟɦɫɹ, ɦɧɨɝɨ ɦɟɧɶɲɟ ɞɪɭɝɨɣ, ɯɚɪɚɤɬɟɪɧɨɣ ɞɥɹ ɷɬɨɣ ɡɚɞɚɱɢ, ɜɟɥɢɱɢɧɵ ɬɨɣ ɠɟ ɪɚɡɦɟɪɧɨɫɬɢ, ɬɨ ɦɨɞɟɥɶ ɜɵɛɪɚɧɚ ɜɟɪɧɨ.
Ɂɚɦɟɬɢɦ, ɱɬɨ ɨɞɢɧ ɢ ɬɨɬ ɠɟ ɦɚɬɟɪɢɚɥɶɧɵɣ ɨɛɴɟɤɬ ɢɥɢ ɨɞɧɨ ɢ ɬɨ ɠɟ ɹɜɥɟɧɢɟ ɜ ɪɚɡɥɢɱɧɵɯ ɭɫɥɨɜɢɹɯ ɦɨɝɭɬ ɛɵɬɶ ɪɚɫɫɦɨɬɪɟɧɵ ɜ ɪɚɦɤɚɯ ɪɚɡɥɢɱɧɵɯ ɦɨɞɟɥɟɣ, ɟɫɥɢ ɨɧɢ ɭɞɨɜɥɟɬɜɨɪɹɸɬ ɤɪɢɬɟɪɢɹɦ ɩɪɚɜɢɥɶɧɨɫɬɢ ɜɵɛɨɪɚ ɷɬɢɯ ɦɨɞɟɥɟɣ.
Ɍɟɥɨ ɨɬɫɱɟɬɚ – ɬɟɥɨ, ɨɬɧɨɫɢɬɟɥɶɧɨ ɤɨɬɨɪɨɝɨ ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɞɜɢɠɟɧɢɟ ɞɪɭɝɢɯ ɬɟɥ.
ɑɚɫɵ – ɧɟɩɨɞɜɢɠɧɵɣ ɨɬɧɨɫɢɬɟɥɶɧɨ ɬɟɥɚ ɨɬɫɱɟɬɚ ɩɪɢɛɨɪ ɞɥɹ ɢɡɦɟɪɟɧɢɹ ɜɪɟɦɟɧɢ, ɩɪɢɧɰɢɩ ɞɟɣɫɬɜɢɹ ɤɨɬɨɪɨɝɨ ɨɫɧɨɜɚɧ ɧɚ ɫɪɚɜɧɟɧɢɢ ɞɥɢɬɟɥɶɧɨɫɬɢ ɢɫɫɥɟɞɭɟɦɨɝɨ ɜɪɟɦɟɧɧɨɝɨ ɢɧɬɟɪɜɚɥɚ ɫ ɞɥɢɬɟɥɶɧɨɫɬɶɸ ɜɵɛɪɚɧɧɨɝɨ ɡɚ ɷɬɚɥɨɧ ɩɟɪɢɨɞɢɱɟɫɤɨɝɨ ɩɪɨɰɟɫɫɚ.
ɋɢɫɬɟɦɚ ɨɬɫɱɟɬɚ – ɫɨɜɨɤɭɩɧɨɫɬɶ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ1, ɫɜɹɡɚɧɧɨɣ ɫ ɬɟɥɨɦ ɨɬɫɱɟɬɚ, ɢ ɧɚɛɨɪɚ ɫɢɧɯɪɨɧɢɡɢɪɨɜɚɧɧɵɯ ɱɚɫɨɜ, ɪɚɡɦɟɳɟɧɧɵɯ ɜ ɪɚɡɧɵɯ ɬɨɱɤɚɯ ɤɨɨɪɞɢɧɚɬɧɨɣ ɫɢɫɬɟɦɵ.
ɍɫɥɨɜɢɟ ɫɢɧɯɪɨɧɢɡɚɰɢɢ ɱɚɫɨɜ A ɢ B, ɪɚɫɩɨɥɨɠɟɧɧɵɯ ɜ ɪɚɡɧɵɯ ɬɨɱɤɚɯ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ (ɜ ɩɪɟɞɩɨɥɨɠɟɧɢɢ ɨɛ ɢɡɨɬɪɨɩɧɨɫɬɢ ɩɪɨɫɬɪɚɧɫɬɜɚ):
1 Ⱦɚɥɟɟ ɜ ɬɟɤɫɬɟ, ɟɫɥɢ ɷɬɨ ɧɟ ɨɝɨɜɚɪɢɜɚɟɬɫɹ ɨɫɨɛɨ, ɢɫɩɨɥɶɡɭɟɬɫɹ ɞɟɤɚɪɬɨɜɚ ɫɢɫɬɟɦɚ ɤɨɨɪɞɢɧɚɬ.
10 ɆȿɏȺɇɂɄȺ. ɆȿɌɈȾɂɄȺ Ɋȿɒȿɇɂə ɁȺȾȺɑ
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Ɂɞɟɫɶ |
– ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɢɡɥɭɱɟɧɢɹ ɢɡ ɬɨɱɤɢ A ɫɜɟɬɨɜɨɝɨ ɫɢɝɧɚ- |
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ɥɚ (ɤɜɚɧɬɚ ɫɜɟɬɚ) ɩɨ ɱɚɫɚɦ ɜ ɬɨɱɤɟ A, t B – ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɪɟɝɢɫɬɪɚɰɢɢ ɷɬɨɝɨ ɫɢɝɧɚɥɚ ɜ ɬɨɱɤɟ B ɩɨ ɱɚɫɚɦ ɜ ɬɨɱɤɟ B, t2A – ɦɨɦɟɧɬ
ɜɪɟɦɟɧɢ ɪɟɝɢɫɬɪɚɰɢɢ ɜ ɬɨɱɤɟ A ɨɬɪɚɠɟɧɧɨɝɨ ɜ ɬɨɱɤɟ B ɫɢɝɧɚɥɚ ɩɨ ɱɚɫɚɦ ɜ ɬɨɱɤɟ A.
Ɇɚɬɟɪɢɚɥɶɧɚɹ ɬɨɱɤɚ – ɮɢɡɢɱɟɫɤɨɟ ɩɨɧɹɬɢɟ (ɦɨɞɟɥɶ, ɚɛɫɬɪɚɤɰɢɹ), ɩɪɟɞɫɬɚɜɥɹɸɳɟɟ ɬɟɥɨ, ɪɚɡɦɟɪɚɦɢ (ɢ ɮɨɪɦɨɣ) ɤɨɬɨɪɨɝɨ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ ɜ ɭɫɥɨɜɢɹɯ ɞɚɧɧɨɣ ɡɚɞɚɱɢ.
ɉɨɥɨɠɟɧɢɟ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɞɚɧɧɨɣ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ (ɜ ɞɚɧɧɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ) S ɡɚɞɚɟɬɫɹ ɟɟ ɤɨɨɪɞɢɧɚɬɚɦɢ ɢɥɢ ɪɚɞɢɭɫ-ɜɟɤɬɨɪɨɦ r .
Ɋɚɞɢɭɫ-ɜɟɤɬɨɪ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ r ɨɬɧɨɫɢɬɟɥɶɧɨ ɞɚɧ-
ɧɨɣ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ – ɜɟɤɬɨɪ, ɧɚɱɚɥɨ ɤɨɬɨɪɨɝɨ ɧɚɯɨɞɢɬɫɹ ɜ ɧɚɱɚɥɟ ɤɨɨɪɞɢɧɚɬ ɷɬɨɣ ɫɢɫɬɟɦɵ, ɚ ɤɨɧɟɰ – ɜ ɦɟɫɬɟ ɪɚɫɩɨɥɨɠɟɧɢɹ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ (ɫɦ. ɪɢɫ. 1.1ɚ):
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j ɢ k – ɨɪɬɵ ɞɟɤɚɪɬɨɜɨɣ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ: |
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k1; x, y, z – ɤɨɨɪɞɢɧɚɬɵ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ.
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Ɋɢɫ. 1.1. Ɋɚɞɢɭɫ-ɜɟɤɬɨɪ r(t) , ɩɟɪɟɦɟɳɟɧɢɟ r(t ǻt) (ɚ) ɢ ɫɤɨɪɨɫɬɶ ȣ(t) |
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ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ |
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Ɂɚɤɨɧ ɞɜɢɠɟɧɢɹ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɞɚɧɧɨɣ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ – ɡɚɜɢɫɢɦɨɫɬɶ ɪɚɞɢɭɫ-ɜɟɤɬɨɪɚ ɢɥɢ ɤɨɨɪɞɢɧɚɬ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ ɨɬ ɜɪɟɦɟɧɢ: