4-ma’ruza qattiq jismning aylanma harakati

Albatta x1 - x2 ayirmasi quyosh va yer orasidagi masofa d ga teng bo’ladi

To simplify the computation let's define our coordinate system such as its origin coincides with the center of the Sun.

H isoblanishlarni soddalashtirish uchun Quyosh markaziga mos keluvchi koordinata sistemasini aniqlaylik.
We can also use an abbreviated notation to write equations for systems with more than two particles.
Ikki jismdan ko’proq jismlar sistemasini og’irlik markazini topish uchun tenglama yozishda qisqartirilgan belgidan foydalanishimiz mumkin.
; ; ,
Shuni ta’kidlab o‘tish kerakki, tizimning inertsiya markazi uning og‘irlik markazi bilan ustma-ust tushishi kerak;
3. Moddiy nuqtalar tizimi inertsiya markazining radius- vektoridan vaqt bo‘yicha birinchi tartibli hosila olinsa, inertsiya markazining tezligi kelib chiqadi:
,
buyerda, ekanini hisobga olsak:
,

bunda tizimning impulsi bo‘lib, tizimdagi moddiy nuqtalar impulslarining geometrik yig‘indisiga teng

(8.5) – ifodadan moddiy nuqtalar tizimining impulsi quyidagiga teng bo‘ladi:

He defined the linear momentum , p, as the product of an object’s mass , m, and its velocity , v.
P harakatga keltiruvchi kuchning chizig’ini , m jismning massasini , vesa jismning tezligini bildiradi.
Note that in this section, we use the term momentum to refer to linear momentum.
Eslatma, bu qismda biz harakatga keltiruvchi kuch chizig’ini tushuntirishda harakatga keltiruvchi kuch terminidan foydalanamiz.

Now let`s look at each type of collision separately and find the final velocity of the objects .
Endi to’qnashishni aloxida va obyektlarning oxirgi tezligini topamiz
,
Bu nihoyatda katta ahamiyatga ega bo‘lgan xulosani keltirib chiqaradi: tizim nuqtalarining hamma massalari, uning inertsiya markaziga to‘plangan holda harakatlanganda, ularning markazga to‘plangan umumiy impulslari qanday bo‘lsa, tizimning to‘la impulsi ham shunga teng bo‘ladi.
Shuning uchun tizimning impulsiga uning inertsiya markazining impulsi ham deyiladi. Tizim inertsiya markazining impulsini (8.7) ifodaga asosan quyidagicha ifodalash mumkin:

Because of conservation of momentum the total initial and final momentums equal each other . Ajralish tufayli dastlabki umumiy moment boshlang’ich momentlarning har biriga teng bo’ladi.

Factoring out the masses, we obtain equation 1.