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Create: 2024-01-17 Update: 2025-06-30 01:03:55

هرگاه بخواهیم کوتاهترین مسیر بین دو نقطه را در فضایی مشخص طی کنیم، باید در راستای ژئودوزیک ها حرکت کنیم. ساده ترین مثال این موضوع خط راست است. در فضای اقلیدسی خط راست کوتاهترین مسیر بین دو نقطه را نشان می‌دهد.

برای بدست آوردن معادله ژئودوزیک می‌توان به این صورت عمل کرد:

ابتدا یادآوری کنم که ضرب داخلی دو بردار مانند u و w در فضایی با متریک g با معادله ۱ بدست می‌آید. برای بدست آوردن عنصر طول ds برحسب پارامتر t از ضرب داخلی بردار سرعت استفاده می‌کنیم. (معادله ۲)
با استفاده از حساب وردش ها می‌توان می‌نیمم طول مسیر بین دو نقطه را با کمینه کردن انتگرال ۳ بدست آورد.
پس از استفاده‌ از فرمول اویلر معادله ژئودوزیک حاصل می‌شود. (معادله۴)

🔹 اگر به قانون دوم نیوتن که به صورت هموردا در «این پست» نوشته شده است دقت کنید متوجه خواهید شد در حالتی که نیروهای وارد بر جسمی صفر باشد معادله مسیر آن همان معادله ژئودوزیک است. بنابراین می‌توان نتیجه گرفت جسم آزاد در راستای ژئودوزیک ها حرکت می‌کند.

🆔 @Physics3p

Quantum Physics

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10.0K viewsMatin Abri, Jan 17, 2024 at 09:22

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Can I mute a Telegram group?

In recent times, Telegram has gained a lot of popularity because of the controversy over WhatsApp’s new privacy policy. In January 2021, Telegram was the most downloaded app worldwide and crossed 500 million monthly active users. And with so many active users on the app, people might get messages in bulk from a group or a channel that can be a little irritating. So to get rid of the same, you can mute groups, chats, and channels on Telegram just like WhatsApp. You can mute notifications for one hour, eight hours, or two days, or you can disable notifications forever.

هرگاه بخواهیم کوتاهترین مسیر بین دو نقطه را در فضایی مشخص طی کنیم، باید در راستای ژئودوزیک ها حرکت کنیم. ساده ترین مثال این موضوع خط راست است. در فضای اقلیدسی خط راست کوتاهترین مسیر بین دو نقطه را نشان می‌دهد.

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