Dimensional analysis is the method of deriving possible equations by analyzing the units of the relevant variables and combining them for the desired output.
The international system of units measures 7 units from which all other units can be constructed.
| Quantity | Unit | Index in vector |
|---|---|---|
| Time | s | 0 |
| Distance | m | 1 |
| Mass | kg | 2 |
| Current | A | 3 |
| Heat | K | 4 |
| Amount | mol | 5 |
| Luminousity | cd | 6 |
By ordering this list and interpreting the powers on each unit as a vector in 7-dimensional Unit-Space we can calculate the powers of each variable.
Once the vectors and the target point are defined a base of the vector space is constructed.
The vector space is 7 dimensional. If n vectors are supplied 7-n linearly independent vectors have to be constructed from the supplied variables to form a complete base.
Writing the base as a Matrix B and the target as the vector t we can calculate the coordinates a in the base B
The dimensional analysis script comes with a simple console application. First make sure you have a version of python 3 installed.
Then go into the /src/ folder and locate the script console_interface.py in the console:
> python3 console_interface.py
Now enter your variables into the console:
Please enter you variables in the following format:
<name> = <amount> [units]
Example: p = 12 kg m^-1 s^(-2)
Please make sure to use SI units specified in the dimensions file.
Variable 1: F = 15 kg*m/s^2
Variable 2:
The Variables should be provided in the following format:
<name> = <amount> <unit 1>^<power 1> * <unit 2>^<power 2> / <unit 3>^<power 3>*...
You can either multiply or divide units with or by each other. Please note that, wile parentheses are accepted in a power you cannot group units with them.
Spaces are optional, but can also be used to multiply units instead of *. If a unit has a power no separator is needed to multiply with the following unit.
Terminate your input by entering an empty line.
Then provide the target dimensions in the format
<amount> <unit 1>^<power 1> * <unit 2>^<power 2> / <unit 3>^<power 3>*...