Теоретическая механика_в_Вопросах_и_Ответах
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ɩɪɨɢɡɜɨɞɧɵɦ ɨɬ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɢ ɫɢɫɬɟɦɵ ɩɨ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦ
ɤɨɨɪɞɢɧɚɬɚɦ ɷɬɨɣ ɬɨɱɤɢ
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Ʉɚɤɢɟɩɨɜɟɪɯɧɨɫɬɢɧɚɡɵɜɚɸɬɫɹɷɤɜɢɩɨɬɟɧɰɢɚɥɶɧɵɦɢɢɤɚɤɨɜɵɢɯɭɪɚɜɧɟɧɢɹ?
Ƚɟɨɦɟɬɪɢɱɟɫɤɨɟ ɦɟɫɬɨ ɬɨɱɟɤ ɩɪɨɫɬɪɚɧɫɬɜɚ, ɜ ɤɨɬɨɪɵɯ ɩɨɬɟɧɰɢɚɥɶɧɚɹ ɷɧɟɪɝɢɹ ɢɦɟɟɬ ɨɞɧɨ ɢ ɬɨ ɠɟ ɡɧɚɱɟɧɢɟ ɧɚɡɵɜɚɟɬɫɹ ɩɨɜɟɪɯɧɨɫɬɶɸ ɪɚɜɧɨɝɨ ɩɨɬɟɧɰɢɚɥɚ ɢɥɢ ɷɤɜɢɜɚɥɟɧɬɧɨɣ ɩɨɜɟɪɯɧɨɫɬɶɸ ɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ
ɉ(xi , yi , zi ) C .
Ʉɚɤ ɧɚɩɪɚɜɥɟɧɚ ɫɢɥɚ, ɞɟɣɫɬɜɭɸɳɚɹ ɧɚ ɦɚɬɟɪɢɚɥɶɧɭɸ ɬɨɱɤɭ ɜ ɩɨɬɟɧɰɢ-
ɚɥɶɧɨɦ ɩɨɥɟ, ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɷɤɜɢɩɨɬɟɧɰɢɚɥɶɧɨɣ ɩɨɜɟɪɯɧɨɫɬɢ, ɩɪɨɯɨɞɹ-
ɳɟɣ ɱɟɪɟɡ ɷɬɭ ɬɨɱɤɭ?
ɋɢɥɚ F ɧɚɩɪɚɜɥɟɧɚ ɩɨ ɧɨɪɦɚɥɢ ɤ ɷɤɜɢɩɨɬɟɧɰɢɚɥɶɧɨɣ ɩɨɜɟɪɯɧɨɫɬɢ, ɩɪɨ-
ɯɨɞɹɳɟɣ ɱɟɪɟɡ ɞɚɧɧɭɸ ɬɨɱɤɭ ɜ ɫɬɨɪɨɧɭ ɭɦɟɧɶɲɟɧɢɹ ɡɧɚɱɟɧɢɣ ɩɨɬɟɧɰɢ-
ɚɥɶɧɨɣ ɷɧɟɪɝɢɢ.
ɑɟɦɭ ɪɚɜɧɚ ɩɨɬɟɧɰɢɚɥɶɧɚɹ ɷɧɟɪɝɢɹ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ ɢ ɦɟɯɚɧɢɱɟɫɤɨɣ
ɫɢɫɬɟɦɵ, ɧɚɯɨɞɹɳɢɯɫɹ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɫɢɥ ɬɹɠɟɫɬɢ?
ɉɨɬɟɧɰɢɚɥɶɧɚɹ ɷɧɟɪɝɢɹ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ, ɧɚɯɨɞɹɳɟɣɫɹ ɩɨɞ ɞɟɣɫɬɜɢ-
ɟɦ ɫɢɥɵ ɬɹɠɟɫɬɢ, ɪɚɜɧɚ
ɉG z C .
ɉɨɬɟɧɰɢɚɥɶɧɚɹ ɷɧɟɪɝɢɹ ɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ, ɧɚɯɨɞɹɳɟɣɫɹ ɩɨɞ ɞɟɣɫɬ-
ɜɢɟɦ ɫɢɥɵ ɬɹɠɟɫɬɢ, ɪɚɜɧɚ ɩɪɨɢɡɜɟɞɟɧɢɸ ɜɟɫɚ ɫɢɫɬɟɦɵ ɧɚ ɜɵɫɨɬɭ ɟɟ ɰɟɧ-
ɬɪɚ ɦɚɫɫ ɧɚɞ ɧɭɥɟɜɨɣ ɷɤɜɢɩɨɬɟɧɰɢɚɥɶɧɨɣ ɩɨɜɟɪɯɧɨɫɬɶɸ
ɉG zC .
Ʉɚɤɨɣ ɜɢɞ ɢɦɟɸɬ ɷɤɜɢɩɨɬɟɧɰɢɚɥɶɧɵɟ ɩɨɜɟɪɯɧɨɫɬɢ ɩɨɥɹ ɫɢɥɵ ɬɹɠɟɫɬɢ ɢ
ɧɶɸɬɨɧɨɜɨɣ ɫɢɥɵ ɬɹɝɨɬɟɧɢɹ?
71
ɗɤɜɢɩɨɬɟɧɰɢɚɥɶɧɵɟ ɩɨɜɟɪɯɧɨɫɬɢ ɩɨɥɹ ɫɢɥɵ ɬɹɠɟɫɬɢ ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨ-
ɛɨɣ ɝɨɪɢɡɨɧɬɚɥɶɧɵɟ ɩɥɨɫɤɨɫɬɢ. ɋɢɥɚ ɬɹɠɟɫɬɢ ɧɚɩɪɚɜɥɟɧɚ ɩɟɪɩɟɧɞɢɤɭ-
ɥɹɪɧɨ ɷɬɢɦ ɩɥɨɫɤɨɫɬɹɦ ɜ ɫɬɨɪɨɧɭ ɭɦɟɧɶɲɟɧɢɹ ɡɧɚɱɟɧɢɣ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɢ.
ɗɤɜɢɩɨɬɟɧɰɢɚɥɶɧɵɟ ɩɨɜɟɪɯɧɨɫɬɢ ɩɨɥɹ ɫɢɥɵ ɩɪɢɬɹɠɟɧɢɹ ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣ ɫɮɟɪɢɱɟɫɤɢɟ ɩɨɜɟɪɯɧɨɫɬɢ ɫ ɰɟɧɬɪɨɦ ɜ ɬɨɱɤɟ O. ɍɪɚɜɧɟɧɢɟ ɷɤɜɢ-
ɩɨɬɟɧɰɢɚɥɶɧɵɯ ɩɨɜɟɪɯɧɨɫɬɟɣ ɢɦɟɟɬ ɜɢɞ
rconst .
ȼɱɟɦ ɡɚɤɥɸɱɚɟɬɫɹ ɡɚɤɨɧ ɫɨɯɪɚɧɟɧɢɹ ɢ ɩɪɟɜɪɚɳɟɧɢɹ ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ?
ɉɪɢ ɞɜɢɠɟɧɢɢ ɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ɜ ɫɬɚɰɢɨɧɚɪɧɨɦ ɩɨɬɟɧɰɢɚɥɶɧɨɦ
ɩɨɥɟ ɩɨɥɧɚɹ ɦɟɯɚɧɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɫɢɫɬɟɦɵ ɩɪɢ ɞɜɢɠɟɧɢɢ ɨɫɬɚɟɬɫɹ ɩɨ-
ɫɬɨɹɧɧɨɣ.
T ɉ const .
ɉɨɱɟɦɭ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɰɟɧɬɪɚɥɶɧɨɣ ɫɢɥɵ ɦɚɬɟɪɢɚɥɶɧɚɹ ɬɨɱɤɚ ɨɩɢɫɵɜɚɟɬ
ɩɥɨɫɤɭɸ ɤɪɢɜɭɸ?
ȿɫɥɢ ɦɚɬɟɪɢɚɥɶɧɚɹ ɬɨɱɤɚ ɞɜɢɠɟɬɫɹ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɰɟɧɬɪɚɥɶɧɨɣ ɫɢɥɵ, ɬɨ ɦɨɦɟɧɬ ɤɨɥɢɱɟɫɬɜɚ ɞɜɢɠɟɧɢɹ ɬɨɱɤɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɰɟɧɬɪɚ ɩɨɫɬɨɹɧɟɧ ɢ ɬɨɱɤɚ ɞɜɢɠɟɬɫɹ ɜ ɩɥɨɫɤɨɫɬɢ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɣ ɜɟɤɬɨɪɭ lO .
ɑɬɨ ɧɚɡɵɜɚɸɬ ɫɟɤɬɨɪɧɨɣ ɫɤɨɪɨɫɬɶɸ ɢ ɤɚɤ ɜɵɪɚɡɢɬɶ ɟɟ ɦɨɞɭɥɶ ɜ ɩɨɥɹɪ-
ɧɵɯ ɤɨɨɪɞɢɧɚɬɚɯ?
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ȼɟɥɢɱɢɧɚ |
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ɧɚɡɵɜɚɟɬɫɹ ɫɟɤɬɨɪɧɨɣ ɫɤɨɪɨɫɬɶɸ. |
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ȼ ɱɟɦ ɡɚɤɥɸɱɚɟɬɫɹ ɡɚɤɨɧ ɩɥɨɳɚɞɟɣ?
ɉɪɢ ɞɜɢɠɟɧɢɢ ɬɨɱɤɢ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɰɟɧɬɪɚɥɶɧɨɣ ɫɢɥɵ ɩɥɨɳɚɞɶ, ɨɩɢɫɵɜɚ-
ɟɬɫɹɪɚɞɢɭɫɨɦ — ɜɟɤɬɨɪɨɦɬɨɱɤɢ, ɢɡɦɟɧɹɟɬɫɹɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɜɪɟɦɟɧɢ
Fct FO .
72
Ʉɚɤɨɣ ɜɢɞ ɢɦɟɟɬ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɟ ɭɪɚɜɧɟɧɢɟ ɜ ɮɨɪɦɟ Ȼɢɧɟ, ɨɩɪɟɞɟɥɹɸ-
ɳɟɟ ɬɪɚɟɤɬɨɪɢɸ ɬɨɱɤɢ, ɞɜɢɠɭɳɟɣɫɹ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɰɟɧɬɪɚɥɶɧɨɣ ɫɢɥɵ?
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ɍɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɬɨɱɤɢ ɜ ɮɨɪɦɟ Ȼɢɧɟ: |
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dM |
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4mc |
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ȼ ɫɥɭɱɚɟ ɩɪɢɬɹɠɟɧɢɹ, ɤɨɝɞɚ Pr 0 , ɬɪɚɟɤɬɨɪɢɹ ɨɛɪɚɳɟɧɚ ɤ ɩɨɥɸɫɭ O ɜɨ-
ɝɧɭɬɨɫɬɶɸ.
ɉɪɢɧɰɢɩ Ⱦɚɥɚɦɛɟɪɚ.
ȼ ɱɟɦ ɡɚɤɥɸɱɚɟɬɫɹ ɫɭɳɧɨɫɬɶ ɩɪɢɧɰɢɩɚ Ƚɟɪɦɚɧɚ — ɗɣɥɟɪɚ — Ⱦɚɥɚɦɛɟɪɚ
ɞɥɹ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ?
Ƚɟɨɦɟɬɪɢɱɟɫɤɚɹ ɫɭɦɦɚ ɜɫɟɯ ɩɪɢɥɨɠɟɧɧɵɯ ɤ ɬɨɱɤɟ ɫɢɥ ɢ ɫɢɥɵ ɢɧɟɪɰɢɢ
ɷɬɨɣ ɬɨɱɤɢ ɪɚɜɧɵ ɧɭɥɸ.
¦Fk Ɏ 0.
Ʉɚɤɢɦ ɭɫɥɨɜɢɹɦ ɭɞɨɜɥɟɬɜɨɪɹɸɬ ɜ ɥɸɛɨɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɝɥɚɜɧɵɟ ɜɟɤɬɨ-
ɪɵ ɜɧɟɲɧɢɯ ɡɚɞɚɜɚɟɦɵɯ ɫɢɥ, ɪɟɚɤɰɢɣ ɫɜɹɡɟɣ ɢ ɫɢɥ ɢɧɟɪɰɢɢ ɬɨɱɟɤ ɧɟɫɜɨɛɨɞ-
ɧɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ɢ ɝɥɚɜɧɵɟ ɦɨɦɟɧɬɵ ɷɬɢɯ ɫɢɥ ɨɬɧɨɫɢɬɟɥɶɧɨ ɥɸɛɨɝɨ ɧɟɩɨɞɜɢɠɧɨɝɨ ɰɟɧɬɪɚ?
ȼ ɥɸɛɨɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɝɟɨɦɟɬɪɢɱɟɫɤɚɹ ɫɭɦɦɚ ɝɥɚɜɧɵɯ ɜɟɤɬɨɪɨɜ ɡɚɞɚ-
ɜɚɟɦɵɯ ɫɢɥ, ɪɟɚɤɰɢɣ ɫɜɹɡɟɣ ɢ ɫɢɥ ɢɧɟɪɰɢɢ ɬɨɱɟɤ ɫɢɫɬɟɦɵ ɪɚɜɧɵ ɧɭɥɸ.
ȼ ɥɸɛɨɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɞɥɹ ɜɫɹɤɨɣ ɧɟɫɜɨɛɨɞɧɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ɝɟɨɦɟɬɪɢɱɟɫɤɚɹ ɫɭɦɦɚ ɝɥɚɜɧɵɯ ɦɨɦɟɧɬɨɜ ɡɚɞɚɜɚɟɦɵɯ ɫɢɥ, ɪɟɚɤɰɢɣ ɫɜɹɡɟɣ ɢɫɢɥɢɧɟɪɰɢɢɨɬɧɨɫɢɬɟɥɶɧɨ ɥɸɛɨɝɨɧɟɩɨɞɜɢɠɧɨɝɨɰɟɧɬɪɚɪɚɜɧɚɧɭɥɸ.
Ʉɚɤɨɜɵ ɦɨɞɭɥɶ ɢ ɧɚɩɪɚɜɥɟɧɢɟ ɝɥɚɜɧɨɝɨ ɜɟɤɬɨɪɚ ɫɢɥ ɢɧɟɪɰɢɢ ɦɟɯɚɧɢɱɟɫɤɨɣ
ɫɢɫɬɟɦɵ?
Ƚɥɚɜɧɵɣ ɜɟɤɬɨɪ ɫɢɥ ɢɧɟɪɰɢɢ ɪɚɜɟɧ:
Ɏ maC .
Ɇɨɞɭɥɶ ɝɥɚɜɧɨɝɨ ɜɟɤɬɨɪɚ ɫɢɥ ɢɧɟɪɰɢɢ
73
ɎmaC .
Ʉɱɟɦɭ ɩɪɢɜɨɞɹɬɫɹ ɫɢɥɵ ɢɧɟɪɰɢɢ ɬɨɱɟɤ ɬɜɟɪɞɨɝɨ ɬɟɥɚ:
ɚ) ɩɪɢ ɩɨɫɬɭɩɚɬɟɥɶɧɨɦ ɞɜɢɠɟɧɢɢ ɬɟɥɚ;
ɩɪɢ ɩɨɫɬɭɩɚɬɟɥɶɧɨɦ ɞɜɢɠɟɧɢɢ ɫɢɥɵ ɢɧɟɪɰɢɢ ɩɪɢɜɨɞɹɬɫɹ ɤ ɪɚɜɧɨɞɟɣɫɬ-
ɜɭɸɳɟɣ ɫɢɥɟ, ɩɪɢɥɨɠɟɧɧɨɣ ɜ ɰɟɧɬɪɟ ɦɚɫɫ ɬɟɥɚ, ɪɚɜɧɨɣ ɩɨ ɦɨɞɭɥɸ ɩɪɨ-
ɢɡɜɟɞɟɧɢɸ ɦɚɫɫɵ ɬɟɥɚ ɧɚ ɦɨɞɭɥɶ ɭɫɤɨɪɟɧɢɹ ɟɝɨ ɰɟɧɬɪɚ ɦɚɫɫ ɢ ɧɚɩɪɚɜɥɟ-
ɧɵ ɩɪɨɬɢɜɨɩɨɥɨɠɧɨ ɷɬɨɦɭ ɭɫɤɨɪɟɧɢɸ;
ɛ) ɩɪɢ ɜɪɚɳɟɧɢɢ ɬɟɥɚ, ɢɦɟɸɳɟɝɨ ɩɥɨɫɤɨɫɬɶ ɦɚɬɟɪɢɚɥɶɧɨɣ ɫɢɦɦɟɬɪɢɢ, ɜɨ-
ɤɪɭɝ ɧɟɩɨɞɜɢɠɧɨɣ ɨɫɢ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɣ ɷɬɨɣ ɩɥɨɫɤɨɫɬɢ;
ɩɪɢ ɜɪɚɳɟɧɢɢ ɬɜɟɪɞɨɝɨ ɬɟɥɚ, ɢɦɟɸɳɟɝɨ ɩɥɨɫɤɨɫɬɶ ɦɚɬɟɪɢɚɥɶɧɨɣ ɫɢɦ-
ɦɟɬɪɢɢ, ɜɨɤɪɭɝ ɨɫɢ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɣ ɷɬɨɣ ɩɥɨɫɤɨɫɬɢ, ɫɢɥɵ ɢɧɟɪɰɢɢ ɩɪɢɜɨɞɹɬɫɹ ɤ ɪɚɜɧɨɞɟɣɫɬɜɭɸɳɟɣ ɫɢɥɟ, ɥɟɠɚɳɟɣ ɜ ɩɥɨɫɤɨɫɬɢ ɫɢɦɦɟɬɪɢɢ.
Ɇɨɞɭɥɶ ɢ ɧɚɩɪɚɜɥɟɧɢɟ ɷɬɨɣ ɫɢɥɵ ɪɚɜɧɵ ɝɥɚɜɧɨɦɭ ɜɟɤɬɨɪɭ ɫɢɥ ɢɧɟɪɰɢɢ,
ɚ ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɟɟ ɥɢɧɢɢ ɞɟɣɫɬɜɢɹ ɞɨ ɬɨɱɤɢ ɩɟɪɟɫɟɱɟɧɢɹ ɨɫɢ ɜɪɚɳɟɧɢɹ ɫ ɩɥɨɫɤɨɫɬɶɸ ɫɢɦɦɟɬɪɢɢ ɪɚɜɧɨ
hM Ɏ ;
Ɏ
ɜ) ɩɪɢ ɩɥɨɫɤɨɦ ɞɜɢɠɟɧɢɢ ɬɟɥɚ, ɢɦɟɸɳɟɝɨ ɩɥɨɫɤɨɫɬɶ ɦɚɬɟɪɢɚɥɶɧɨɣ ɫɢɦ-
ɦɟɬɪɢɢ?
ȿɫɥɢ ɬɜɟɪɞɨɟ ɬɟɥɨ, ɢɦɟɸɳɟɟ ɩɥɨɫɤɨɫɬɶ ɦɚɬɟɪɢɚɥɶɧɨɣ ɫɢɦɦɟɬɪɢɢ, ɞɜɢ-
ɠɟɬɫɹ ɩɚɪɚɥɥɟɥɶɧɨ ɷɬɨɣ ɩɥɨɫɤɨɫɬɢ, ɬɨ ɫɢɥɵ ɢɧɟɪɰɢɢ ɩɪɢɜɨɞɹɬɫɹ ɤ ɫɢɥɟ,
ɩɪɢɥɨɠɟɧɧɨɣ ɜ ɰɟɧɬɪɟ ɦɚɫɫ ɢ ɪɚɜɧɨɣ ɝɥɚɜɧɨɦɭ ɜɟɤɬɨɪɭ ɫɢɥ ɢɧɟɪ-
ɰɢɢɎ maC , ɢ ɤ ɩɚɪɟ ɫɢɥ, ɥɟɠɚɳɟɣ ɜ ɩɥɨɫɤɨɫɬɢ ɫɢɦɦɟɬɪɢɢ, ɱɢɫɥɨɜɨɟ ɡɧɚɱɟɧɢɟ ɦɨɦɟɧɬɚ ɤɨɬɨɪɨɣ ɨɩɪɟɞɟɥɹɟɬɫɹ ɮɨɪɦɭɥɨɣ:
M Ɏ ICH .
74
ɉɪɢ ɤɚɤɢɯ ɭɫɥɨɜɢɹɯ ɞɢɧɚɦɢɱɟɫɤɢɟ ɞɚɜɥɟɧɢɹ ɜɪɚɳɚɸɳɟɝɨɫɹ ɬɟɥɚ ɧɚ ɨɩɨɪɵ
ɪɚɜɧɵ ɧɭɥɸ?
Ⱦɢɧɚɦɢɱɟɫɤɢɟ ɫɨɫɬɚɜɥɹɸɳɢɟ ɪɟɚɤɰɢɣ ɩɨɞɲɢɩɧɢɤɨɜ ɪɚɜɧɵ ɧɭɥɸ ɜ ɬɨɦ
ɫɥɭɱɚɟ, ɟɫɥɢ ɨɫɶ ɜɪɚɳɟɧɢɹ ɬɟɥɚ ɹɜɥɹɟɬɫɹ ɝɥɚɜɧɨɣ ɰɟɧɬɪɚɥɶɧɨɣ ɨɫɶɸ ɢɧɟɪ-
ɰɢɢ ɬɟɥɚ.
ɉɪɢɧɰɢɩ ɜɨɡɦɨɠɧɵɯ ɩɟɪɟɦɟɳɟɧɢɣ.
ɑɬɨ ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣ ɨɛɨɛɳɟɧɧɵɟ ɤɨɨɪɞɢɧɚɬɵ ɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ?
ɇɟɡɚɜɢɫɢɦɵɟ ɜɟɥɢɱɢɧɵ qi , ɨɞɧɨɡɧɚɱɧɨ ɨɩɪɟɞɟɥɹɸɳɢɟ ɩɨɥɨɠɟɧɢɟ ɜɫɟɯ ɬɨɱɟɤ ɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ɧɚɡɵɜɚɸɬɫɹ ɨɛɨɛɳɟɧɧɵɦɢ ɤɨɨɪɞɢɧɚɬɚɦɢ ɷɬɨɣ ɫɢɫɬɟɦɵ.
ɑɟɦɭ ɪɚɜɧɨ ɱɢɫɥɨ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ ɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ?
Ⱦɥɹ ɝɨɥɨɧɨɦɧɵɯ ɫɢɫɬɟɦ ɱɢɫɥɨ ɧɟɡɚɜɢɫɢɦɵɯ ɨɛɨɛɳɟɧɧɵɯ ɤɨɨɪɞɢɧɚɬ qi
ɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ɪɚɜɧɨ ɱɢɫɥɭ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ ɷɬɨɣ ɫɢɫɬɟɦɵ.
ȼ ɤɚɤɨɦ ɫɥɭɱɚɟ ɞɟɤɚɪɬɨɜɵ ɤɨɨɪɞɢɧɚɬɵ ɬɨɱɟɤ ɫɢɫɬɟɦɵ ɡɚɜɢɫɹɬ ɧɟ ɬɨɥɶɤɨ
ɨɬ ɨɛɨɛɳɟɧɧɵɯ ɤɨɨɪɞɢɧɚɬ, ɧɨ ɢ ɨɬ ɜɪɟɦɟɧɢ?
ɉɪɢ ɧɚɥɢɱɢɢ ɧɟɫɬɚɰɢɨɧɚɪɧɵɯ ɫɜɹɡɟɣ ɞɟɤɚɪɬɨɜɵ ɤɨɨɪɞɢɧɚɬɵ ɜɫɟɯ ɬɨɱɟɤ
ɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ɹɜɥɹɸɬɫɹ ɮɭɧɤɰɢɹɦɢ ɧɟ ɬɨɥɶɤɨ ɨɛɨɛɳɟɧɧɵɯ ɤɨ-
ɨɪɞɢɧɚɬ, ɧɨ ɢ ɜɪɟɦɟɧɢ
xi |
xi q1,q2...qs ,t , |
yi |
yi q1,q2...qs ,t , |
zi |
zi q1,q2...qs ,t . |
ɑɬɨ ɧɚɡɵɜɚɸɬ ɜɨɡɦɨɠɧɵɦɢ ɩɟɪɟɦɟɳɟɧɢɹɦɢ ɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ?
ȼɨɡɦɨɠɧɵɦɢ (ɢɥɢ ɜɢɪɬɭɚɥɶɧɵɦɢ) ɩɟɪɟɦɟɳɟɧɢɹɦɢ ɧɟɫɜɨɛɨɞɧɨɣ ɦɟɯɚ-
ɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ɧɚɡɵɜɚɸɬɫɹ ɜɨɨɛɪɚɠɚɟɦɵɟ ɛɟɫɤɨɧɟɱɧɨ ɦɚɥɵɟ ɩɟɪɟ-
ɦɟɳɟɧɢɹ, ɞɨɩɭɫɤɚɟɦɵɟ ɧɚɥɨɠɟɧɧɵɦɢ ɧɚ ɫɢɫɬɟɦɭ ɫɜɹɡɹɦɢ.
75
Ɂɚɜɢɫɹɬ ɥɢ ɜɨɡɦɨɠɧɵɟ ɩɟɪɟɦɟɳɟɧɢɹ ɨɬ ɞɟɣɫɬɜɭɸɳɢɯ ɧɚ ɫɢɫɬɟɦɭ ɫɢɥ?
ȼɨɡɦɨɠɧɵɟ ɩɟɪɟɦɟɳɟɧɢɹ ɨɬ ɞɟɣɫɬɜɭɸɳɢɯ ɫɢɥ ɧɟ ɡɚɜɢɫɹɬ.
Ʉɚɤɢɟ ɫɜɹɡɢ ɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ɧɚɡɵɜɚɸɬ ɢɞɟɚɥɶɧɵɦɢ?
ȿɫɥɢ ɫɭɦɦɚ ɪɚɛɨɬ ɪɟɚɤɰɢɣ ɫɜɹɡɟɣ ɧɚ ɥɸɛɨɦ ɜɨɡɦɨɠɧɨɦ ɩɟɪɟɦɟɳɟɧɢɢ
ɫɢɫɬɟɦɵ ɪɚɜɧɚ ɧɭɥɸ, ɬɨ ɬɚɤɢɟ ɫɜɹɡɢ ɧɚɡɵɜɚɸɬɫɹ ɢɞɟɚɥɶɧɵɦɢ.
ɉɨɱɟɦɭ ɫɜɹɡɶ, ɨɫɭɳɟɫɬɜɥɟɧɧɚɹ ɫ ɬɪɟɧɢɟɦ, ɧɟ ɹɜɥɹɟɬɫɹ ɢɞɟɚɥɶɧɨɣ ɫɜɹɡɶɸ?
Ɍɚɤ ɤɚɤ ɜɨɡɦɨɠɧɨɟ ɩɟɪɟɦɟɳɟɧɢɟ ɬɨɱɤɢ ɩɪɢɥɨɠɟɧɢɹ ɫɢɥɵ ɬɪɟɧɢɹ ɥɟɠɢɬ ɜ ɩɥɨɫɤɨɫɬɢ, ɤɚɫɚɬɟɥɶɧɨɣ ɨɩɨɪɧɨɣ ɩɨɜɟɪɯɧɨɫɬɢ, ɢ ɫɢɥɚ ɬɪɟɧɢɹ ɥɟɠɢɬ ɜ ɷɬɨɣ ɠɟ ɩɥɨɫɤɨɫɬɢ, ɪɚɛɨɬɚ ɫɢɥɵ ɬɪɟɧɢɹ Fɬɪ GS z 0 ɢ ɭɫɥɨɜɢɟ ɢɞɟɚɥɶɧɨ-
ɫɬɢ ɫɜɹɡɟɣ ɧɟ ɜɵɩɨɥɧɹɟɬɫɹ.
Ʉɚɤ ɮɨɪɦɭɥɢɪɭɟɬɫɹ ɩɪɢɧɰɢɩ ɜɨɡɦɨɠɧɵɯ ɩɟɪɟɦɟɳɟɧɢɣ?
ɇɟɨɛɯɨɞɢɦɨɟ ɢ ɞɨɫɬɚɬɨɱɧɨɟ ɭɫɥɨɜɢɟ ɪɚɜɧɨɜɟɫɢɹ ɫɢɫɬɟɦɵ ɫɢɥ, ɩɪɢɥɨ-
ɠɟɧɧɵɯ ɤ ɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɟ, ɩɨɞɱɢɧɟɧɧɨɣ ɫɬɚɰɢɨɧɚɪɧɵɦ ɞɜɭɫɬɨ-
ɪɨɧɧɢɦ ɢ ɢɞɟɚɥɶɧɵɦ ɫɜɹɡɹɦ, ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɪɚɜɟɧɫɬɜɟ ɧɭɥɸ ɫɭɦɦɵ ɷɥɟ-
ɦɟɧɬɚɪɧɵɯ ɪɚɛɨɬ ɡɚɞɚɜɚɟɦɵɯ ɫɢɥ ɧɚ ɥɸɛɨɦ ɜɨɡɦɨɠɧɨɦ ɩɟɪɟɦɟɳɟɧɢɢ ɫɢɫɬɟɦɵ ɢɡ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɝɨ ɟɟ ɩɨɥɨɠɟɧɢɹ.
Ʉɚɤɢɟ ɜɢɞɵ ɦɨɠɟɬ ɢɦɟɬɶ ɭɪɚɜɧɟɧɢɟ ɪɚɛɨɬ?
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ɉɨɱɟɦɭ ɩɪɢɧɰɢɩ ɜɨɡɦɨɠɧɵɯ ɩɟɪɟɦɟɳɟɧɢɣ ɭɩɪɨɳɚɟɬ ɜɵɜɨɞ ɭɫɥɨɜɢɣ ɪɚɜɧɨ-
ɜɟɫɢɹ ɫɢɥ, ɩɪɢɥɨɠɟɧɧɵɯ ɤ ɧɟɫɜɨɛɨɞɧɵɦ ɫɢɫɬɟɦɚɦ, ɫɨɫɬɨɹɳɢɦ ɢɡ ɛɨɥɶɲɨɝɨ ɱɢɫɥɚ ɬɟɥ?
ȿɫɥɢ ɫɢɫɬɟɦɚ, ɫɨɫɬɨɹɳɚɹ ɢɡ ɛɨɥɶɲɨɝɨ ɱɢɫɥɚ ɬɟɥ, ɢɦɟɟɬ ɨɞɧɭ ɫɬɟɩɟɧɶ ɫɜɨɛɨɞɵ, ɬɨ ɩɪɢɧɰɢɩ ɜɨɡɦɨɠɧɵɯ ɩɟɪɟɦɟɳɟɧɢɣ ɭɫɬɚɧɚɜɥɢɜɚɟɬ ɫɪɚɡɭ ɭɫ-
ɥɨɜɢɟ ɪɚɜɧɨɜɟɫɢɹ ɡɚɞɚɜɚɟɦɵɯ ɫɢɥ, ɩɪɢɥɨɠɟɧɧɵɯ ɤ ɫɢɫɬɟɦɟ.
76
Ʉɚɤ ɫɨɫɬɚɜɥɹɸɬɫɹ ɭɪɚɜɧɟɧɢɹ ɪɚɛɨɬ ɞɥɹ ɫɢɥ, ɞɟɣɫɬɜɭɸɳɢɯ ɧɚ ɦɟɯɚɧɢɱɟ-
ɫɤɭɸ ɫɢɫɬɟɦɭ ɫ ɧɟɫɤɨɥɶɤɢɦɢ ɫɬɟɩɟɧɹɦɢ ɫɜɨɛɨɞɵ?
ȿɫɥɢ ɫɢɫɬɟɦɚ ɢɦɟɟɬ ɧɟɫɤɨɥɶɤɨ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ, ɬɨ ɭɪɚɜɧɟɧɢɹ ɪɚɛɨɬ ɫɨ-
ɫɬɚɜɥɹɸɬɫɹ ɞɥɹ ɤɚɠɞɨɝɨ ɧɟɡɚɜɢɫɢɦɨɝɨ ɩɟɪɟɦɟɳɟɧɢɹ ɫɢɫɬɟɦɵ ɜ ɨɬɞɟɥɶ-
ɧɨɫɬɢ ɢ ɩɨɥɭɱɚɟɬɫɹ ɫɬɨɥɶɤɨ ɭɫɥɨɜɢɣ ɪɚɜɧɨɜɟɫɢɹ, ɫɤɨɥɶɤɨ ɫɬɟɩɟɧɟɣ ɫɜɨ-
ɛɨɞɵ ɢɦɟɟɬ ɦɟɯɚɧɢɱɟɫɤɚɹ ɫɢɫɬɟɦɚ.
Ʉɚɤɨɜɚ ɡɚɜɢɫɢɦɨɫɬɶ ɦɟɠɞɭ ɞɜɢɠɭɳɟɣ ɫɢɥɨɣ ɢ ɫɢɥɨɣ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɜ ɩɪɨ-
ɫɬɟɣɲɢɯ ɦɚɲɢɧɚɯ?
Ⱦɥɹ ɭɫɬɚɧɨɜɥɟɧɢɹ ɡɚɜɢɫɢɦɨɫɬɢ ɞɜɢɠɭɳɟɣ ɫɢɥɵ F ɢɥɢ ɜɪɚɳɚɸɳɟɝɨ ɦɨ-
ɦɟɧɬɚ Mɜɪ ɢ ɫɢɥɵ ɫɨɩɪɨɬɢɜɥɟɧɢɹ R ɢɥɢ ɦɨɦɟɧɬɚ ɫɨɩɪɨɬɢɜɥɟɧɢɹ Mɫɨɩɪ
ɫɨɨɛɳɚɟɬ ɦɚɲɢɧɟ ɜɨɡɦɨɠɧɨɟ ɩɟɪɟɦɟɳɟɧɢɟ ɢ ɫɨɫɬɚɜɥɹɸɬ ɭɪɚɜɧɟɧɢɟ ɪɚɛɨɬ
F G rF R G rR 0 ɢɥɢ Mɜɪ GM Mɫɨɩɪ GM 0.
Ʉɚɤ ɮɨɪɦɭɥɢɪɭɟɬɫɹ ɡɨɥɨɬɨɟ ɩɪɚɜɢɥɨ ɦɟɯɚɧɢɤɢ?
Ɍɨ, ɱɬɨ ɜɵɢɝɪɵɜɚɟɬɫɹ ɜ ɫɢɥɟ, ɬɟɪɹɟɬɫɹ ɜ ɫɤɨɪɨɫɬɢ:
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Ʉɚɤɢɦ ɨɛɪɚɡɨɦ ɨɩɪɟɞɟɥɹɸɬ ɪɟɚɤɰɢɢ ɫɜɹɡɟɣ ɫ ɩɨɦɨɳɶɸ ɩɪɢɧɰɢɩɚ ɜɨɡɦɨɠ-
ɧɵɯ ɩɟɪɟɦɟɳɟɧɢɣ?
Ɉɬɛɪɚɫɵɜɚɸɬ ɬɭ ɫɜɹɡɶ, ɪɟɚɤɰɢɸ ɤɨɬɨɪɨɣ ɬɪɟɛɭɟɬɫɹ ɨɩɪɟɞɟɥɢɬɶ. Ⱦɟɣɫɬ-
ɜɢɟ ɫɜɹɡɢ ɡɚɦɟɧɹɸɬ ɪɟɚɤɰɢɟɣ, ɤɨɬɨɪɚɹ ɩɟɪɟɯɨɞɢɬ ɜ ɱɢɫɥɨ ɡɚɞɚɜɚɟɦɵɯ ɫɢɥ. ɋɢɫɬɟɦɟ ɫɨɨɛɳɚɸɬ ɜɨɡɦɨɠɧɨɟ ɩɟɪɟɦɟɳɟɧɢɟ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɟ ɩɨ-
ɥɭɱɟɧɧɨɣ ɫɬɟɩɟɧɢ ɫɜɨɛɨɞɵ. ɋɨɫɬɚɜɥɹɸɬ ɭɪɚɜɧɟɧɢɟ ɪɚɛɨɬ, ɜ ɤɨɬɨɪɨɟ ɜɯɨ-
ɞɹɬ ɡɚɞɚɜɚɟɦɵɟ ɫɢɥɵ ɢ ɪɟɚɤɰɢɹ ɨɬɛɪɨɲɟɧɧɨɣ ɫɜɹɡɢ. ɂɡ ɷɬɨɝɨ ɭɪɚɜɧɟɧɢɹ ɨɩɪɟɞɟɥɹɸɬ ɢɫɤɨɦɭɸ ɪɟɚɤɰɢɸ.
Ɉɛɳɟɟ ɭɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ.
Ʉɚɤɨɣ ɜɢɞ ɢɦɟɟɬ ɨɛɳɟɟ ɭɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ?
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Ɉɛɳɟɟ ɭɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɜ ɥɸɛɨɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɫɭɦɦɚ ɪɚɛɨɬ ɜɫɟɯ ɡɚɞɚɜɚɟɦɵɯ ɫɢɥ ɢ ɫɢɥ ɢɧɟɪɰɢɢ ɬɨɱɟɤ ɧɟɫɜɨɛɨɞɧɨɣ ɦɟ-
ɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ɫ ɞɜɭɫɬɨɪɨɧɧɢɦɢ ɢɞɟɚɥɶɧɵɦɢ ɫɜɹɡɹɦɢ ɧɚ ɥɸɛɨɦ ɜɨɡɦɨɠɧɨɦ ɟɟ ɩɟɪɟɦɟɳɟɧɢɢ ɪɚɜɧɚ ɧɭɥɸ.
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ɑɬɨ ɧɚɡɵɜɚɟɬɫɹ ɨɛɨɛɳɟɧɧɨɣ ɫɢɥɨɣ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɧɟɤɨɬɨɪɨɣ ɨɛɨɛɳɟɧɧɨɣ ɤɨɨɪɞɢɧɚɬɟ ɫɢɫɬɟɦɵ, ɢ ɤɚɤɭɸ ɨɧɚ ɢɦɟɟɬ ɪɚɡɦɟɪɧɨɫɬɶ?
Ɉɛɨɛɳɟɧɧɨɣ ɫɢɥɨɣ Qj , ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɨɛɨɛɳɟɧɧɨɣ ɤɨɨɪɞɢɧɚɬɟ qj ,
ɧɚɡɵɜɚɸɬ ɫɤɚɥɹɪɧɭɸ ɜɟɥɢɱɢɧɭ, ɨɩɪɟɞɟɥɹɟɦɭɸ ɨɬɧɨɲɟɧɢɟɦ ɷɥɟɦɟɧɬɚɪ-
ɧɨɣ ɪɚɛɨɬɵ ɞɟɣɫɬɜɭɸɳɢɯ ɫɢɥ ɧɚ ɩɟɪɟɦɟɳɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ,
ɜɵɡɜɚɧɧɨɟ ɷɥɟɦɟɧɬɚɪɧɵɦ ɩɪɢɪɚɳɟɧɢɟɦ ɤɨɨɪɞɢɧɚɬɵ qj ɤ ɜɟɥɢɱɢɧɟ ɷɬɨɝɨ
ɩɪɢɪɚɳɟɧɢɹ
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Ɋɚɡɦɟɪɧɨɫɬɶ ɨɛɨɛɳɟɧɧɨɣ ɫɢɥɵ ɡɚɜɢɫɢɬ ɨɬ ɪɚɡɦɟɪɧɨɫɬɢ ɨɛɨɛɳɟɧɧɨɣ ɤɨ-
ɨɪɞɢɧɚɬɵ qj .
ɑɟɦɭ ɪɚɜɧɵ ɨɛɨɛɳɟɧɧɵɟ ɪɟɚɤɰɢɢ ɢɞɟɚɥɶɧɵɯ ɫɜɹɡɟɣ?
ȼ ɫɥɭɱɚɟ ɫɬɚɰɢɨɧɚɪɧɵɯ ɫɜɹɡɟɣ ɨɛɨɛɳɟɧɧɵɟ ɪɟɚɤɰɢɢ ɢɞɟɚɥɶɧɵɯ ɫɜɹɡɟɣ
ɪɚɜɧɵ ɧɭɥɸ.
Ɂɚɩɢɲɢɬɟ ɨɛɳɟɟ ɭɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ ɜ ɨɛɨɛɳɟɧɧɵɯ ɫɢɥɚɯ.
Ɉɛɳɟɟ ɭɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ ɜ ɨɛɨɛɳɟɧɧɵɯ ɫɢɥɚɯ ɢɦɟɟɬ ɜɢɞ:
s |
Gqj 0 ɢɥɢ Qj QɎj 0, ( j 1...s) . |
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Ʉɚɤɨɣ ɜɢɞ ɢɦɟɸɬ ɭɫɥɨɜɢɹ ɪɚɜɧɨɜɟɫɢɹ ɫɢɥ, ɩɪɢɥɨɠɟɧɧɵɯ ɤ ɦɟɯɚɧɢɱɟɫɤɨɣ
ɫɢɫɬɟɦɟ, ɩɨɥɭɱɟɧɧɵɟ ɢɡ ɨɛɳɟɝɨ ɭɪɚɜɧɟɧɢɹ ɞɢɧɚɦɢɤɢ ɜ ɨɛɨɛɳɟɧɧɵɯ ɫɢɥɚɯ?
ȿɫɥɢ ɦɟɯɚɧɢɱɟɫɤɚɹ ɫɢɫɬɟɦɚ ɧɚɯɨɞɢɬɫɹ ɜ ɫɨɫɬɨɹɧɢɢ ɩɨɤɨɹ ɢɥɢ ɪɚɜɧɨɦɟɪ-
ɧɨɝɨ ɩɪɹɦɨɥɢɧɟɣɧɨɝɨ ɞɜɢɠɟɧɢɹ, ɭɫɥɨɜɢɹ ɪɚɜɧɨɜɟɫɢɹ ɢɦɟɸɬ ɜɢɞ:
Qj 0, ( j 1...s).
Ʉɚɤɢɦɢ ɮɨɪɦɭɥɚɦɢ ɜɵɪɚɠɚɸɬɫɹ ɨɛɨɛɳɟɧɧɵɟ ɫɢɥɵ ɱɟɪɟɡ ɩɪɨɟɤɰɢɢ ɫɢɥ ɧɚ ɧɟɩɨɞɜɢɠɧɵɟ ɨɫɢ ɞɟɤɚɪɬɨɜɵɯ ɤɨɨɪɞɢɧɚɬ?
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Ʉɚɤ ɨɩɪɟɞɟɥɹɸɬɫɹ ɨɛɨɛɳɟɧɧɵɟ ɫɢɥɵ ɜ ɫɥɭɱɚɟ ɤɨɧɫɟɪɜɚɬɢɜɧɵɯ ɢ ɜ ɫɥɭɱɚɟ ɧɟɤɨɧɫɟɪɜɚɬɢɜɧɵɯ ɫɢɥ?
ȼ ɫɥɭɱɚɟ ɤɨɧɫɟɪɜɚɬɢɜɧɵɯ ɫɢɥ Qj |
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Ʉɚɤɨɜ ɜɢɞ ɭɫɥɨɜɢɣ ɪɚɜɧɨɜɟɫɢɹ ɫɢɥ, ɢɦɟɸɳɢɯ ɩɨɬɟɧɰɢɚɥ?
wɉ 0 ( j 1...s). wqj
Ⱦɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟɭɪɚɜɧɟɧɢɹɜɨɛɨɛɳɟɧɧɵɯɤɨɨɪɞɢɧɚɬɚɯ.
Ɏɭɧɤɰɢɟɣ ɤɚɤɢɯ ɚɪɝɭɦɟɧɬɨɜ ɹɜɥɹɟɬɫɹ ɜɟɤɬɨɪ ɫɤɨɪɨɫɬɢ ɬɨɱɤɢ, ɩɪɢɧɚɞɥɟ-
ɠɚɳɟɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɟ ɫ s ɫɬɟɩɟɧɹɦɢ ɫɜɨɛɨɞɵ?
ȼ ɫɥɭɱɚɟ ɫɬɚɰɢɨɧɚɪɧɵɯ ɫɜɹɡɟɣ ɜɟɤɬɨɪ ɫɤɨɪɨɫɬɢ ɬɨɱɤɢ ɹɜɥɹɟɬɫɹ ɮɭɧɤɰɢɟɣ
ɨɛɨɛɳɟɧɧɵɯ ɫɤɨɪɨɫɬɟɣ ɢ ɨɛɨɛɳɟɧɧɵɯ ɤɨɨɪɞɢɧɚɬ
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ɑɟɦɭ ɪɚɜɧɚ ɱɚɫɬɧɚɹ ɩɪɨɢɡɜɨɞɧɚɹ ɨɬ ɜɟɤɬɨɪɚ ɫɤɨɪɨɫɬɢ ɬɨɱɤɢ ɫɢɫɬɟɦɵ ɩɨ
ɤɚɤɨɣ-ɥɢɛɨ ɨɛɨɛɳɟɧɧɨɣ ɫɤɨɪɨɫɬɢ?
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Ɏɭɧɤɰɢɟɣ ɤɚɤɢɯ ɚɪɝɭɦɟɧɬɨɜ ɹɜɥɹɟɬɫɹ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɫɢɫɬɟɦɵ,
ɩɨɞɱɢɧɟɧɧɨɣ ɝɨɥɨɧɨɦɧɵɦ ɧɟɫɬɚɰɢɨɧɚɪɧɵɦ ɫɜɹɡɹɦ?
Ʉɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɜ ɫɥɭɱɚɟ ɝɨɥɨɧɨɦɧɵɯ ɧɟɫɬɚɰɢɨɧɚɪɧɵɯ ɫɜɹɡɟɣ ɹɜɥɹɟɬɫɹ
ɮɭɧɤɰɢɟɣɨɛɨɛɳɟɧɧɵɯɤɨɨɪɞɢɧɚɬ, ɨɛɨɛɳɟɧɧɵɯɫɤɨɪɨɫɬɟɣɢɜɪɟɦɟɧɢ:
TT qs ,qs ,t .
Ʉɚɤɨɣ ɜɢɞ ɢɦɟɸɬ ɭɪɚɜɧɟɧɢɹ Ʌɚɝɪɚɧɠɚ ɜɬɨɪɨɝɨ ɪɨɞɚ? ɑɟɦɭ ɪɚɜɧɨ ɱɢɫɥɨ
ɷɬɢɯ ɭɪɚɜɧɟɧɢɣ ɞɥɹ ɤɚɠɞɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ?
d § wT · |
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ɑɢɫɥɨ ɭɪɚɜɧɟɧɢɣ Ʌɚɝɪɚɧɠɚ ɜɬɨɪɨɝɨ ɪɨɞɚ ɪɚɜɧɨ ɱɢɫɥɭ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ.
Ʉɚɤɨɣ ɜɢɞ ɩɪɢɧɢɦɚɸɬ ɭɪɚɜɧɟɧɢɹ Ʌɚɝɪɚɧɠɚ ɜɬɨɪɨɝɨ ɪɨɞɚ ɜ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɧɚ ɫɢɫɬɟɦɭ ɞɟɣɫɬɜɭɸɬ ɨɞɧɨɜɪɟɦɟɧɧɨ ɤɨɧɫɟɪɜɚɬɢɜɧɵɟ ɢ ɧɟɤɨɧɫɟɪɜɚɬɢɜ-
ɧɵɟ ɫɢɥɵ?
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ɑɬɨ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɮɭɧɤɰɢɹ Ʌɚɝɪɚɧɠɚ, ɢɥɢ ɤɢɧɟɬɢɱɟɫɤɢɣ ɩɨɬɟɧɰɢɚɥ?
Ʉɢɧɟɬɢɱɟɫɤɢɣ ɩɨɬɟɧɰɢɚɥ ɹɜɥɹɟɬɫɹ ɮɭɧɤɰɢɟɣ ɨɛɨɛɳɟɧɧɵɯ ɤɨɨɪɞɢɧɚɬ,
ɨɛɨɛɳɟɧɧɵɯ ɫɤɨɪɨɫɬɟɣ ɢ ɜɪɟɦɟɧɢ.
L L(qs ,qs ,t) Ɍ ɉ.
Ʉɚɤɨɣ ɜɢɞ ɢɦɟɸɬ ɭɪɚɜɧɟɧɢɹ Ʌɚɝɪɚɧɠɚ ɜɬɨɪɨɝɨ ɪɨɞɚ ɞɥɹ ɤɨɧɫɟɪɜɚɬɢɜɧɨɣ ɫɢɫɬɟɦɵ?
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