book:chap1:1.2_dimensional_analysis
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| book:chap1:1.2_dimensional_analysis [2021/10/25 22:52] – jv | book:chap1:1.2_dimensional_analysis [2022/04/01 19:28] (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 ]] | ||
| + | |||
| + | ---- | ||
| + | |||
| ===== 1.2 Dimensional analysis ===== | ===== 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. | The discussion of a more advanced formulation may appear as a homework problem later on on this course. | ||
| - | <WRAP box round> | + | <WRAP box round # |
| A dynamics with $n$ parameters, | A dynamics with $n$ parameters, | ||
| where the positions $\mathbf q$ and the parameters involve the three units meter, seconds and kilogram, | where the positions $\mathbf q$ and the parameters involve the three units meter, seconds and kilogram, | ||
| Line 14: | Line 23: | ||
| with $n-3$ parameters, | with $n-3$ parameters, | ||
| where the positions $\boldsymbol\xi$, | where the positions $\boldsymbol\xi$, | ||
| - | 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. | are given solely by numbers. | ||
| </ | </ | ||
book/chap1/1.2_dimensional_analysis.1635195155.txt.gz · Last modified: 2021/10/25 22:52 by jv