Theoretical Mechanics IPSP

Jürgen Vollmer, Universität Leipzig

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book:chap1:1.1_basic_notions_of_mechanics

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book:chap1:1.1_basic_notions_of_mechanics [2021/10/25 22:54] – jvbook:chap1:1.1_basic_notions_of_mechanics [2024/10/26 12:19] (current) – jv
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 +[[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 ]]
 +
 +----
 +
 ===== 1.1 Basic notions of mechanics ===== ===== 1.1 Basic notions of mechanics =====
  
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 <wrap lo>**Remark.**  <wrap lo>**Remark.** 
-The arrows indicate here that $\mathbf x_i$ describes a position in space. +Bold-face symbols indicate here that $\mathbf x_i$ describes a position in space. 
-For a $D$-dimensional space one needs $D$ numbers((Strictly speaking we do not only need numbers, but must also indicate the adopted units.))+For a $D$-dimensional space one needs $D$ numbers((Strictly speaking we do not only need numbers,  
 +but must also indicate the adopted units.))
 to specify the position, to specify the position,
 and $\mathbf x_i$ may be thought of as a vector in $\mathbb{R}^D$. and $\mathbf x_i$ may be thought of as a vector in $\mathbb{R}^D$.
-We say that $\mathbf x_i$ is a $D$-vector. +We say that $\mathbf x_i$ is a $D$-vector. 
 +In [[book:chap2:forcestorques|Chapter 2]] we will take a closer look at vectors and their properties.
 </wrap> </wrap>
  
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 the latter will also be denoted as $\dot{\mathbf x}$. the latter will also be denoted as $\dot{\mathbf x}$.
 </wrap> </wrap>
 +
 +<wrap lo>**Remark.** 
 +In hand writing vectors are commonly denoted by an arrow, i.e., $\vec x$
 +rather than $\mathbf x$. 
 +</wrap>
 +
  
 <WRAP box round>**Example 1.1** <wrap hi>A piece of chalk</wrap> \\  <WRAP box round>**Example 1.1** <wrap hi>A piece of chalk</wrap> \\ 
-We wish to follow the trajectory of a piece of chalk through the lecture hall.+We wish to follow the trajectory of a piece of chalk through the lecture hall (i.e., when it is thrown, **not** when somebody is using it to write on a blackboard).
 In order to follow its position and orientation in space, we //decide// to model it In order to follow its position and orientation in space, we //decide// to model it
 as a set of two masses that are localized at the tip and at the tail of the chalk. as a set of two masses that are localized at the tip and at the tail of the chalk.
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 </WRAP> </WRAP>
  
-<WRAP box round>**Definition 1.6** <wrap em>Initial Conditions (IC)</wrap> \\ +<WRAP box round #Defi_IC>**Definition 1.6** <wrap em>Initial Conditions (IC)</wrap> \\ 
 equations of motion}} equations of motion}}
 ordinary differential equation}} ordinary differential equation}}
book/chap1/1.1_basic_notions_of_mechanics.1635195264.txt.gz · Last modified: 2021/10/25 22:54 by jv