Haqiqatan ham sistemaga shunday mumkin bo’lgan ko’chish beramizki, . Bularni (1.11) tenglamaga qo’yib, tenglamaga kelamiz. Shartga ko’ra demak, . Xuddi shunday qolgan umumlashgan kuchlarning ham nolga teng bo’lishini ko’rsatish mumkin.
(1.12) shartdan quyidagi xulosa kelib chiqadi: ideal, statsionar golonom va qo’yib yuborilmaydigan mexanik sistema muvozanatda bo’lishi uchun sistemaning hamma umumlashgan kuchlari nolga teng bo’lishi zarur va yetarli.
Agar mexanik sistemaga ta’sir etuvchi kuchlar konservativ bo’lsa, (1.10) tenglamaga asosan (1.12) tenglamalar quyidagi ko’rinishga keladi:
![](data:image/png;base64,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) (1.13)
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