method_dynamics
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ɋɭɦɦɚ ɪɚɛɨɬ ɜɫɟɯ ɜɧɭɬɪɟɧɧɢɯ ɫɢɥ ɜ ɬɜɟɪɞɨɦ ɬɟɥɟ ɪɚɜɧɚ ɧɭɥɸ.
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ɝɞɟ ɉ(x, y, z) – ɩɨɬɟɧɰɢɚɥɶɧɚɹ ɷɧɟɪɝɢɹ ɬɨɱɤɢ; |
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rPh , ɝɞɟ h – ɜɵɫɨɬɚ ɰɟɧɬɪɚ ɬɹɠɟɫɬɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɭɥɟɜɨɣ ɩɨɜɟɪɯɧɨɫɬɢ, c'2
2 .
ɉɪɢɪɚɳɟɧɢɟ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɫɢɫɬɟɦɵ ɩɪɢ ɩɟɪɟɦɟɳɟɧɢɢ ɟɟ ɢɡ ɨɞɧɨɝɨ ɩɨɥɨɠɟɧɢɹ ɜ ɞɪɭɝɨɟ ɪɚɜɧɨ ɫɭɦɦɟ ɪɚɛɨɬ, ɩɪɨɢɡɜɟɞɟɧɧɵɯ ɧɚ ɷɬɨɦ ɩɟɪɟɦɟɳɟɧɢɢ ɜɫɟɦɢ ɫɢɥɚɦɢ, ɩɪɢɥɨɠɟɧɧɵɦɢ ɤ ɫɢɫɬɟɦɟ, ɬ.ɟ. T2 – T1 = A12.
ɉɪɨɢɡɜɨɞɧɚɹ ɨɬ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɫɢɫɬɟɦɵ ɪɚɜɧɚ ɫɭɦɦɟ ɦɨɳɧɨɫɬɟɣ
ɜɫɟɯ ɫɢɥ, ɞɟɣɫɬɜɭɸɳɢɯ ɧɚ ɷɬɭ ɫɢɫɬɟɦɭ, ɬ.ɟ. |
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ȿɫɥɢ ɫɢɫɬɟɦɚ ɞɜɢɠɟɬɫɹ ɜ ɩɨɬɟɧɰɢɚɥɶɧɨɦ ɫɢɥɨɜɨɦ ɩɨɥɟ, ɬɨ ɩɨɥɧɚɹ ɦɟɯɚɧɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ, ɪɚɜɧɚɹ ɫɭɦɦɟ ɤɢɧɟɬɢɱɟɫɤɨɣ ɢ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɣ, ɨɫɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɨɣ, ɬ. ɟ. Ɍ + ɉ = const.
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Qj (j = 1, 2, ... , s), |
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dt ©wq j ¹ |
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ɝɞɟ q1, q2,..., qS – ɨɛɨɛɳɟɧɧɵɟ ɤɨɨɪɞɢɧɚɬɵ ɫɢɫɬɟɦɵ; s – ɱɢɫɥɨ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ ɫɢɫɬɟɦɵ;
q1, q2 ,…, qS – ɨɛɨɛɳɟɧɧɵɟ ɫɤɨɪɨɫɬɢ;
d
dt
Ɍ – ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɫɢɫɬɟɦɵ; Q1, Q2, ..., QS – ɨɛɨɛɳɟɧɧɵɟ ɫɢɥɵ.
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0, ɝɞɟ L = T – ɉ – ɮɭɧɤɰɢɹ Ʌɚɝɪɚɧɠɚ. |
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©wq j ¹ |
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Ⱦɥɹ ɫɨɫɬɚɜɥɟɧɢɹ ɭɪɚɜɧɟɧɢɣ Ʌɚɝɪɚɧɠɚ ɫɥɟɞɭɟɬ:
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ξɭɫɬɚɧɨɜɢɬɶ ɱɢɫɥɨ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ ɢ ɜɵɛɪɚɬɶ ɨɛɨɛɳɟɧɧɵɟ ɤɨɨɪɞɢɧɚɬɵ;
ξɩɪɟɞɩɨɥɨɠɢɜ, ɱɬɨ ɫɢɫɬɟɦɚ ɞɜɢɠɟɬɫɹ ɬɚɤ, ɱɬɨ ɜɫɟ ɨɛɨɛɳɟɧɧɵɟ ɤɨɨɪɞɢɧɚɬɵ ɭɜɟɥɢɱɢɜɚɸɬɫɹ, ɫɨɫɬɚɜɢɬɶ ɜɵɪɚɠɟɧɢɹ ɞɥɹ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɫɢɫɬɟɦɵ, ɩɪɢ ɷɬɨɦ ɜɫɟ ɩɟɪɟɦɟɧɧɵɟ ɜɟɥɢɱɢɧɵ, ɜɯɨɞɹɳɢɟ ɜ Ɍ, ɞɨɥɠɧɵ ɛɵɬɶ ɜɵɪɚɠɟɧɵ ɱɟɪɟɡ ɨɛɨɛɳɟɧɧɵɟ ɤɨɨɪɞɢɧɚɬɵ ɢ ɨɛɨɛɳɟɧɧɵɟ ɫɤɨɪɨɫɬɢ, ɬ. ɟ. T T(q1,q2 ,...,qS ;q1,q2 ,...,qS ;t) (ɜ ɫɥɭɱɚɟ ɫɬɚɰɢɨɧɚɪɧɵɯ ɫɜɹɡɟɣ ɜɪɟɦɹ t ɧɟ ɜɯɨɞɢɬ ɜ ɜɵɪɚɠɟɧɢɟ T);
ξ ɨɩɪɟɞɟɥɢɬɶ ɱɚɫɬɧɵɟ ɩɪɨɢɡɜɨɞɧɵɟ
d |
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ɫɱɢɬɚɹ ɜɫɟ ɩɟɪɟɦɟɧɧɵɟ, |
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dt ©wq j ¹ |
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wT
wq j ; ɨɩɪɟɞɟɥɢɬɶ ɩɪɨɢɡɜɨɞɧɵɟ
wT
ɜɯɨɞɹɳɢɟ ɜ wq j , ɮɭɧɤɰɢɹɦɢ
ɜɪɟɦɟɧɢ t;
ξ ɧɚɣɬɢ ɨɛɨɛɳɟɧɧɵɟ ɫɢɥɵ; ɩɨɞɫɬɚɜɢɬɶ ɜɫɟ ɧɚɣɞɟɧɧɵɟ ɜɟɥɢɱɢɧɵ ɜ ɢɫɯɨɞɧɨɟ ɭɪɚɜɧɟɧɢɟ.
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ɋɩɢɫɨɤ ɪɟɤɨɦɟɧɞɭɟɦɨɣ ɥɢɬɟɪɚɬɭɪɵ
Ɉɫɧɨɜɧɚɹ ɥɢɬɟɪɚɬɭɪɚ
1. Ɍɚɪɝ ɋ.Ɇ. Ʉɪɚɬɤɢɣ ɤɭɪɫ ɬɟɨɪɟɬɢɱɟɫɤɨɣ ɦɟɯɚɧɢɤɢ : ɭɱɟɛ. ɞɥɹ ɫɬɭɞ. ɜɬɭɡɨɜ / ɋ.Ɇ. Ɍɚɪɝ. – 12-ɟ ɢɡɞ., ɫɬɟɪ. – Ɇ. : ȼɵɫɲ. ɲɤ., 2002. – 416 ɫ.
2. Ɇɟɳɟɪɫɤɢɣ ɂ.ȼ. Ɂɚɞɚɱɢ ɩɨ ɬɟɨɪɟɬɢɱɟɫɤɨɣ ɦɟɯɚɧɢɤɟ : ɭɱɟɛ. ɩɨɫɨɛɢɟ ɞɥɹ ɫɬɭɞ. ɜɭɡɨɜ, ɨɛɭɱ. ɩɨ ɬɟɯɧ. ɫɩɟɰɢɚɥɶɧɨɫɬɹɦ / ɂ.ȼ. Ɇɟɳɟɪɫɤɢɣ ; ɩɨɞ ɪɟɞ. ȼ.Ⱥ. ɉɚɥɶɦɨɜɚ, Ⱦ.Ɋ. Ɇɟɪɤɢɧɚ. – ɋɉɛ. : Ʌɚɧɶ, 2004. – 447 ɫ.
3. əɛɥɨɧɫɤɢɣ Ⱥ.Ⱥ. Ʉɭɪɫ ɬɟɨɪɟɬɢɱɟɫɤɨɣ ɦɟɯɚɧɢɤɢ : ɭɱɟɛ. ɩɨɫɨɛɢɟ ɞɥɹ ɫɬɭɞ. ɜɭɡɨɜ, ɨɛɭɱ. ɩɨ ɬɟɯɧ. ɫɩɟɰɢɚɥɶɧɨɫɬɹɦ / Ⱥ.Ⱥ. əɛɥɨɧɫɤɢɣ, ȼ.Ɇ. ɇɢɤɢɮɨɪɨɜɚ. – 8-ɟ ɢɡɞ., ɫɬɟɪ. – ɋɉɛ. : Ʌɚɧɶ, 2001. – 763 ɫ.
Ⱦɨɩɨɥɧɢɬɟɥɶɧɚɹ ɥɢɬɟɪɚɬɭɪɚ
4.ɋɛɨɪɧɢɤ ɡɚɞɚɧɢɣ ɞɥɹ ɤɭɪɫɨɜɵɯ ɪɚɛɨɬ ɩɨ ɬɟɨɪɟɬɢɱɟɫɤɨɣ ɦɟɯɚɧɢɤɟ : ɭɱɟɛ. ɩɨɫɨɛɢɟ ɞɥɹ ɫɬɭɞ. ɜɬɭɡɨɜ / Ⱥ.Ⱥ. əɛɥɨɧɫɤɢɣ [ɢ ɞɪ.]. – Ɇ. : ɂɧɬɟɝɪɚɥ-ɉɪɟɫɫ, 2004. – 382 ɫ.
5.Ȼɚɬɶ Ɇ.ɂ. Ɍɟɨɪɟɬɢɱɟɫɤɚɹ ɦɟɯɚɧɢɤɚ ɜ ɩɪɢɦɟɪɚɯ ɢ ɡɚɞɚɱɚɯ : ɭɱɟɛ. ɩɨɫɨɛɢɟ ɞɥɹ ɫɬɭɞ. ɜɬɭɡɨɜ : ɜ 3 ɬ. / Ɇ.ɂ. Ȼɚɬɶ, Ƚ.ɘ. Ⱦɠɚɧɟɥɢɞɡɟ, Ⱥ.ɋ. Ʉɟɥɶɡɨɧ. – Ɇ. : ɇɚɭɤɚ, 1990. – Ɍ. 1 : ɋɬɚɬɢɤɚ ɢ ɤɢɧɟɦɚɬɢɤɚ. – 670 ɫ.
6.Ʉɪɚɬɤɢɣ ɫɩɪɚɜɨɱɧɢɤ ɞɥɹ ɢɧɠɟɧɟɪɨɜ ɢ ɫɬɭɞɟɧɬɨɜ. ȼɵɫɲɚɹ ɦɚɬɟɦɚɬɢɤɚ. Ɏɢɡɢɤɚ. Ɍɟɨɪɟɬɢɱɟɫɤɚɹ ɦɟɯɚɧɢɤɚ. ɋɨɩɪɨɬɢɜɥɟɧɢɟ ɦɚɬɟɪɢɚɥɨɜ / Ⱥ.Ⱦ. ɉɨɥɹɧɢɧ [ɢ ɞɪ.]. – Ɇ. : Ɇɟɠɞɭɧɚɪ. ɩɪɨɝɪ. ɨɛɪɚɡɨɜɚɧɢɹ, 1996. – 431 ɫ.
7.Ȼɭɯɝɨɥɶɰ ɇ.ɇ. Ɉɫɧɨɜɧɨɣ ɤɭɪɫ ɬɟɨɪɟɬɢɱɟɫɤɨɣ ɦɟɯɚɧɢɤɢ : ɭɱɟɛ. ɞɥɹ ɝɨɫ. ɭɧ-ɬɨɜ / ɇ.ɇ. Ȼɭɯɝɨɥɶɰ; ɜ ɩɟɪɟɪɚɛɨɬɤɟ ɢ ɫ ɞɨɩ. ɋ.Ɇ. Ɍɚɪɝɚ. – Ɇ. : ɇɚɭɤɚ, 1972. – ɑ. 1 : Ʉɢɧɟɦɚɬɢɤɚ, ɫɬɚɬɢɤɚ, ɞɢɧɚɦɢɤɚ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ. – 467 ɫ.
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ɍɱɟɛɧɨɟ ɢɡɞɚɧɢɟ
Ɋȿɒȿɇɂȿ ɁȺȾȺɑ ɉɈ ɌȿɈɊȿɌɂɑȿɋɄɈɃ ɆȿɏȺɇɂɄȿ. ɑɚɫɬɶ 3. Ⱦɢɧɚɦɢɤɚ
ɍɱɟɛɧɨ-ɦɟɬɨɞɢɱɟɫɤɨɟ ɩɨɫɨɛɢɟ ɞɥɹ ɜɭɡɨɜ
ɋɨɫɬɚɜɢɬɟɥɢ: ɑɟɛɨɬɚɪɟɜ Ⱥɧɞɪɟɣ ɋɟɪɝɟɟɜɢɱ, ɓɟɝɥɨɜɚ ɘɥɢɹ Ⱦɦɢɬɪɢɟɜɧɚ
ɉɨɞɩɢɫɚɧɨ ɜ ɩɟɱɚɬɶ 15.08.07. Ɏɨɪɦɚɬ 60×84/16. ɍɫɥ. ɩɟɱ. ɥ. 3,1. Ɍɢɪɚɠ 100 ɷɤɡ. Ɂɚɤɚɡ 1678.
ɂɡɞɚɬɟɥɶɫɤɨ-ɩɨɥɢɝɪɚɮɢɱɟɫɤɢɣ ɰɟɧɬɪ ȼɨɪɨɧɟɠɫɤɨɝɨ ɝɨɫɭɞɚɪɫɬɜɟɧɧɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ.
394000, ɝ. ȼɨɪɨɧɟɠ, ɩɥ. ɢɦ. Ʌɟɧɢɧɚ, 10. Ɍɟɥ. 208-298, 598-026 (ɮɚɤɫ) http://www.ppc.vsu.ru; e-mail: pp_center@typ.vsu.ru
Ɉɬɩɟɱɚɬɚɧɨ ɜ ɬɢɩɨɝɪɚɮɢɢ ɂɡɞɚɬɟɥɶɫɤɨ-ɩɨɥɢɝɪɚɮɢɱɟɫɤɨɝɨ ɰɟɧɬɪɚ ȼɨɪɨɧɟɠɫɤɨɝɨ ɝɨɫɭɞɚɪɫɬɜɟɧɧɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ.
394000, ɝ. ȼɨɪɨɧɟɠ, ɭɥ. ɉɭɲɤɢɧɫɤɚɹ, 3. Ɍɟɥ. 204-133.
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