From af9371e31497b02abd0b5602c8220816ce03ffcb Mon Sep 17 00:00:00 2001
From: justanothercatgirl <sotov@twistea.su>
Date: Wed, 8 Jan 2025 17:33:12 +0300
Subject: commit 2

---
 oldmech2025.tex | 25 +++++++++++++++++++++++++
 1 file changed, 25 insertions(+)
 create mode 100644 oldmech2025.tex

(limited to 'oldmech2025.tex')

diff --git a/oldmech2025.tex b/oldmech2025.tex
new file mode 100644
index 0000000..866a2a1
--- /dev/null
+++ b/oldmech2025.tex
@@ -0,0 +1,25 @@
+\documentclass[12pt]{article}
+\usepackage{fontspec}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{amsfonts} 
+\usepackage{wrapfig}
+\usepackage{graphicx}
+\usepackage{pifont}
+\newcommand{\cmark}{\ding{51}}%
+\newcommand{\xmark}{\ding{55}}%
+\usepackage[margin=0.4in]{geometry}
+\setmainfont{FreeSans}
+\graphicspath{ {../images} }
+
+\begin{document}
+2. Энергия частицы в релятивистском случае. Связь энергии, импульса
+и массы.
+\begin{itemize}
+	\setlength\itemsep{0cm}
+	\item $p=m\frac{d\vec r}{d \tau} = m\frac{d \{dx, dy, dz\}}{\sqrt{1 - \frac {v^2}{c^2}}dt} = \gamma m\vec v \hspace{1cm}
+		m\frac{d \vec p}{dt} = \vec F \implies \vec F = \gamma'm\vec v + \gamma m \frac {d\vec v}{dt} = \gamma m \vec a + \frac{\gamma^3mv \dot v}{c^2}\vec v\\
+		\vec v \frac{d(\gamma m \vec v)}{dt} = \vec v \vec F,\quad E = \gamma mc^2,\quad E^2 = [v^2 = \frac{p^2c^2}{c^2m^2 + p^2}] = m^2c^4 + p^2c^2,\quad p = \vec v \frac E {c^2}$
+\end{itemize}
+\end{document}
+
-- 
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