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--- book:chap1:1.2_dimensional_analysis [2021/10/25 22:50] – jv
+++ book:chap1:1.2_dimensional_analysis [2022/04/01 19:28] (current) – jv
@@ Line 1: / Line 1: @@
+[[basics| 1. Basic Principles]]
+  * [[ 1.1 Basic notions of mechanics ]]
+  * ** 1.2 Dimensional analysis **
+  * [[ 1.3 Order-of-magnitude guesses ]]
+  * [[ 1.4 Problems ]]
+  * [[ 1.5  Further reading ]]
+----
 ===== 1.2 Dimensional analysis =====
@@ Line 8: / Line 17: @@
 The discussion of a more advanced formulation may appear as a homework problem later on on this course.
-<WRAP box round>**Theorem 1.1 <wrap hi>Buckingham-Pi-Theorem</wrap>** \\
+<WRAP box round #Buckingham-Pi>**Theorem 1.1 <wrap hi>Buckingham-Pi-Theorem</wrap>** \\
 A dynamics with $n$ parameters,
 where the positions $\mathbf q$ and the parameters involve the three units meter, seconds and kilogram,
@@ Line 14: / Line 23: @@
 with $n-3$ parameters,
 where the positions $\boldsymbol\xi$, velocities $\boldsymbol\zeta$,
-and parameters $\pi_j$ with $j \in \{ 1, \dots, n-1\}$
+and parameters $\pi_j$ with $j \in \{ 1, \dots, n-3\}$
 are given solely by numbers.
 </WRAP>
@@ Line 114: / Line 123: @@
 ** Oscillation period of a particle attached to a spring **
 \\
-In a gravitational field with acceleration $g_{\text{Moon}}=1.6\text{m/s$^2$}$
+In a gravitational field with acceleration $g_{\text{Moon}}=1.6\,\text{m/s$^2$}$
-a particle of mass $M=100\text{g}$
+a particle of mass $M=100\,\text{g}$
-is hanging at a spring with spring constant $k=1.6\text{kg/s$^2$}$.
+is hanging at a spring with spring constant $k=1.6\,\text{kg/s$^2$}$.
 It oscillates with period $T$ when it is slightly pulled downwards and released.
 We describe the oscillation by the distance $x(t)$ from its rest position.
@@ Line 130: / Line 139: @@
 \\
-  -  Light travels with a speed of $c \approx 3 \times 10^{8}\,\text{m/s}$, and it takes 500\text{s} to travel from Sun to Earth. What is the Earth-Sun distance$D$, i.e., one Astronomical Unit (AU) in meters?
+  -  Light travels with a speed of $c \approx 3 \times 10^{8}\,\text{m/s}$, and it takes $500\,\text{s}$ to travel from Sun to Earth. What is the Earth-Sun distance$D$, i.e., one Astronomical Unit (AU) in meters?
   -  The period of the trajectory of the Earth around the Sun depends on $D$, on the mass $M = 2 \times 10^{30}\,\text{kg}$ of the sun, and on the gravitational constant $G = 6.7 \times 10^{-11}\,\text{m$^3$/kg s$^2$}$. Estimate, based on this information, how long it takes for the Earth to travel once around the sun.
   -  Express your estimate in terms of years.  The estimate of (b) is of order one, but still off by a considerable factor. Do you recognize the numerical value of this factor?