Kinetikada **König teoremasi** yoki **Königning parchalanishi** Iogann Samuel König tomonidan olingan matematik munosabat bo'lib, jismlar va zarralar tizimlarining burchak momenti va kinetik energiyalarini hisoblashda yordam beradi.

Zarrachalar tizimi uchun
------------------------

Teorema ikki qismga bo'lingan.

### Kyoning teoremasining birinchi qismi

Birinchi qism tizimning burchak momenti massa markazining burchak momenti va massa markaziga nisbatan zarrachalarga tatbiq etilgan burchak momentining yig'indisi sifatida ifodalaydi. 

{\displaystyle \displaystyle {\vec {L}}={\vec {r}}\_{CoM}\times \sum \limits \_{i}m\_{i}{\vec {v}}\_{CoM}+{\vec {L}}'={\vec {L}}\_{CoM}+{\vec {L}}'}

#### Isbot

Koordinata boshi O bo'lgan inersial sanoq sistemasini hisobga olsak, tizimning burchak momentini quyidagicha aniqlash mumkin:

{\displaystyle {\vec {L}}=\sum \limits \_{i}({\vec {r}}\_{i}\times m\_{i}{\vec {v}}\_{i})}

Bitta zarrachaning joylashishini quyidagicha ifodalash mumkin:

{\displaystyle {\vec {r}}\_{i}={\vec {r}}\_{CoM}+{\vec {r}}'\_{i}}

Shunday qilib, biz bitta zarrachaning tezligini aniqlashimiz mumkin:

{\displaystyle {\vec {v}}\_{i}={\vec {v}}\_{CoM}+{\vec {v}}'\_{i}}

Birinchi tenglama quyidagiga keladi:

{\displaystyle {\vec {L}}=\sum \limits \_{i}({\vec {r}}\_{CoM}+{\vec {r}}'\_{i})\times m\_{i}({\vec {v}}\_{CoM}+{\vec {v}}'\_{i})}
{\displaystyle {\vec {L}}=\sum \limits \_{i}{\vec {r}}'\_{i}\times m\_{i}{\vec {v}}'\_{i}+\left(\sum \limits \_{i}m\_{i}{\vec {r}}'\_{i}\right)\times {\vec {v}}\_{CoM}+{\vec {r}}\_{CoM}\times \sum \limits \_{i}m\_{i}{\vec {v}}'\_{i}+\sum \limits \_{i}{\vec {r}}\_{CoM}\times m\_{i}{\vec {v}}\_{CoM}}
Ammo quyidagi shartlar nolga teng:

{\displaystyle \sum \limits \_{i}m\_{i}{\vec {r}}'\_{i}=0}

{\displaystyle \sum \limits \_{i}m\_{i}{\vec {v}}'\_{i}=0}

Shunday qilib, isbotlandi:

{\displaystyle {\vec {L}}=\sum \limits \_{i}{\vec {r}}'\_{i}\times m\_{i}{\vec {v}}'\_{i}+M{\vec {r}}\_{CoM}\times {\vec {v}}\_{CoM}}

bu yerda M - tizimning umumiy massasi .

Qattiq jism uchun
-----------------

Teoremani qattiq jismlarga ham qo'llash mumkin, bunda ba'zi bir inersial sanoq sistemasida o'rnatilgan N kuzatuvchi tomonidan ko'rilganidek qattiq jismning kinetik energiyasi K, quyidagicha yozilishi mumkin:

{\displaystyle ^{N}K={\frac {1}{2}}m\cdot {^{N}\mathbf {\bar {v}} }\cdot {^{N}\mathbf {\bar {v}} }+{\frac {1}{2}}{^{N}\!\mathbf {\bar {H}} }\cdot ^{N}{\!\!\mathbf {\omega } }^{R}}

bu yerda {\displaystyle {m}} - qattiq jismning massasi; {\displaystyle {^{N}\mathbf {\bar {v}} }} - inersial sanoq sistemasida N o'rnatilgan kuzatuvchi tomonidan ko'rilgan qattiq jismning massa markazining tezligi; {\displaystyle {^{N}\!\mathbf {\bar {H}} }} - N inersial sanoq sistemasidagi qattiq jismning massa markaziga nisbatan burchak impulsi; va {\displaystyle ^{N}{\!\!\mathbf {\omega } }^{R}} - N inersial sanoq sistemasiga nisbatan qattiq jismning burchak tezligi R

Foydalanilgan adabiyotlar ro'yxati
----------------------------------

* Hanno Essen: *Oʻrtacha burchak tezligi* (1992), Qirollik texnologiya instituti mexanika boʻlimi, S-100 44 Stokgolm, Shvetsiya.
* Samuel König (Sam. Koenigio): *De universali principio æquilibrii & motus, in viva reperto, deque nexu inter vim vivam & actionem, utriusque minimo, dissertatio*, Nova acta eruditorum (1751) 125-135, 162-176 ( Arxivlangan ).
* Pol A. Tipler va Gen Moska (2003), Olimlar va muhandislar uchun fizika (qog'oz): 1A jild: Mexanika (Olimlar va muhandislar uchun fizika), WH Freeman Ed.ISBN 0-7167-0900-7

Iqtiboslar
----------

1. ↑  Essén, Hanno (1993). "Average Angular Velocity". *European Journal of Physics* **14** (5): 201–205. doi:10.1088/0143-0807/14/5/002.
2. ↑  Rao, Anil V.*. Dynamics of Particles and Rigid Bodies: A Systematic Approach*. Cambridge University Press — 421 bet.