nondimensionalization

The last three steps are usually specific to the problem where nondimensionalization is applied.

To deal with this, nondimensionalization is applied to various qualities.

In fact, nondimensionalization can suggest the parameters which should be used for analyzing a system.

Although nondimensionalization is well adapted for these problems, it is not restricted to them.

Nondimensionalization can also recover characteristic properties of a system.

In theoretical physics, however, this scruple can be set aside, by a process called nondimensionalization.

Measuring devices are practical examples of nondimensionalization occurring in everyday life.

The process of nondimensionalization has significant applications in the analysis of differential equations.

For this reason, nondimensionalization is rarely used for higher order differential equations.

For example, if a system has an intrinsic resonance frequency, length, or time constant, nondimensionalization can recover these values.

These can be found by nondimensionalization.

Many illustrative examples of nondimensionalization originate from simplifying differential equations.

This is done through nondimensionalization.

It is a nondimensionalization of a shear stress, and is typically denoted or .

Therefore, understanding how nondimensionalization applies to first and second ordered systems allows the properties of higher order systems to be determined through superposition.

Nondimensionalization is the partial or full removal of units from an equation involving physical quantities by a suitable substitution of variables.

(See Nondimensionalization.)

Planck units have profound significance for theoretical physics since they elegantly simplify several recurring algebraic expressions of physical law by nondimensionalization.

Nondimensionalization is not the same as converting extensive quantities in an equation to intensive quantities, since the latter procedure results in variables that still carry units.

Analysis of differential equation models in biology: a case study for clover meristem populations (Application of nondimensionalization to a problem in biology).

In some physical systems, the term scaling is used interchangeably with nondimensionalization, in order to suggest that certain quantities are better measured relative to some appropriate unit.

The nondimensionalization is in order to compare the driving forces of particle motion (shear stress) to the resisting forces that would make it stationary (particle density and size).

Any equation of physical law can be expressed in such a manner to have all dimensional quantities normalized against like dimensioned quantities (called nondimensionalization) resulting in only dimensionless quantities remaining.

A dimensional equation can have the dimensions reduced or eliminated through nondimensionalization, which begins with dimensional analysis, and involves scaling quantities by characteristic units of a system or natural units of nature.

The theorem can be seen as a scheme for nondimensionalization because it provides a method for computing sets of dimensionless parameters from the given variables, even if the form of the equation is still unknown.