Dimensional analysis lets you understand the relationship between different physical quantities in equations. A维—for example, length—is a measure of a physical quantity without a number. Aunit—for example, meter, inch, or mile—assigns a number or measurement to that dimension.
With dimensional analysis you can:
- Work with standard units and unit systems.Unit systems comprise of a set of base units and derived units. The most common unit systems are SI, US, and CGS. For example, SI base units include mass (kg), time (s), length (m), electric current (ampere), and temperature (kelvin). Derived units such as density (\(kg/m^{3}\)) or force (\(kg\ m/s^{2}\)) can be expressed as a combination of the base units. You can perform calculations withbase unitsor createnew units和单位系统。
- Convert between units.In dimensional analysis, a ratio that converts one unit of measure into another without changing the quantity is called aunit conversion factor. For example, the unit conversion factor between inch and cm is 127/50. You can compute unit conversion factors between Celsius, Fahrenheit, and Kelvin and switch between absolute temperature and temperature difference.
- Check for unit consistency.You can use dimensional analysis to check that the equations you derive accurately represent the physics by checking theconsistency of units. Equations with valid physical meaning will have the same units on the left- and right-hand sides.
- Perform scale analysis.You can use dimensional analysis to understand and maintain accuracy in numerical methods—for example, finite difference approximations with numerators and denominators that differ by orders of magnitudes.
- 发现无量纲字符acteristic constants.You can nondimensionalize equations and determine unitless characteristic constants that can be useful in describing the behavior of a system. For example, you can find the damping ratio ζ (zeta) of a mass spring system and use this to describe whether the spring system is underdamped (ζ < 1), overdamped (ζ > 1), or critically damped (ζ = 1).
Units in MATLAB
Symbolic Math Toolbox™ supports over2000 units of measurementand, using theMATLAB Live Editor, displays units in blue type, making them easy to identify. For more information on dimensional analysis, seeSymbolic Math Toolbox.
Units in Simulink and Simscape
金宝app®enables you to specify physical units as signal attributes to ensure the consistency of calculations across the various components of your model. For more information on Simulink units, seeUnit Specification in Simulink Models. Simscape also supports units in the physical modeling environment. For more information, seephysical units.
