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- Nondimensionalization abstract "Nondimensionalization is the partial or full removal of units from an equation involving physical quantities by a suitable substitution of variables. This technique can simplify and parameterize problems where measured units are involved. It is closely related to dimensional analysis. 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. These units refer to quantities intrinsic to the system, rather than units such as SI units. 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.Nondimensionalization can also recover characteristic properties of a system. For example, if a system has an intrinsic resonance frequency, length, or time constant, nondimensionalization can recover these values. The technique is especially useful for systems that can be described by differential equations. One important use is in the analysis of control systems.One of the simplest characteristic units is the doubling time of a system experiencing exponential growth, or conversely the half-life of a system experiencing exponential decay; a more natural pair of characteristic units is mean age/mean lifetime, which correspond to base e rather than base 2.Many illustrative examples of nondimensionalization originate from simplifying differential equations. This is because a large body of physical problems can be formulated in terms of differential equations. Consider the following: List of dynamical systems and differential equations topics List of partial differential equation topics Differential equations of mathematical physicsAlthough nondimensionalization is well adapted for these problems, it is not restricted to them. An example of a non-differential-equation application is dimensional analysis; another example is normalization in statistics.Measuring devices are practical examples of nondimensionalization occurring in everyday life. Measuring devices are calibrated relative to some known unit. Subsequent measurements are made relative to this standard. Then, the absolute value of the measurement is recovered by scaling with respect to the standard.".
- Nondimensionalization wikiPageExternalLink MA50176.pdf.
- Nondimensionalization wikiPageExternalLink 059.
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- Nondimensionalization wikiPageRevisionID "703614626".
- Nondimensionalization wikiPageWikiLink Buckingham_π_theorem.
- Nondimensionalization wikiPageWikiLink Category:Dimensional_analysis.
- Nondimensionalization wikiPageWikiLink Characteristic_polynomial.
- Nondimensionalization wikiPageWikiLink Complex_conjugate.
- Nondimensionalization wikiPageWikiLink Constant_coefficients.
- Nondimensionalization wikiPageWikiLink Control_system.
- Nondimensionalization wikiPageWikiLink Damping_ratio.
- Nondimensionalization wikiPageWikiLink Differential_equation.
- Nondimensionalization wikiPageWikiLink Dimensional_analysis.
- Nondimensionalization wikiPageWikiLink Dimensionless_quantity.
- Nondimensionalization wikiPageWikiLink Doubling_time.
- Nondimensionalization wikiPageWikiLink Electric_charge.
- Nondimensionalization wikiPageWikiLink Equation.
- Nondimensionalization wikiPageWikiLink Errors_and_residuals.
- Nondimensionalization wikiPageWikiLink Exponential_decay.
- Nondimensionalization wikiPageWikiLink Exponential_growth.
- Nondimensionalization wikiPageWikiLink Forcing_function_(differential_equations).
- Nondimensionalization wikiPageWikiLink Frequency.
- Nondimensionalization wikiPageWikiLink Function_(mathematics).
- Nondimensionalization wikiPageWikiLink Ground_state.
- Nondimensionalization wikiPageWikiLink Half-life.
- Nondimensionalization wikiPageWikiLink Harmonic_oscillator.
- Nondimensionalization wikiPageWikiLink Intensive_and_extensive_properties.
- Nondimensionalization wikiPageWikiLink International_System_of_Units.
- Nondimensionalization wikiPageWikiLink Length.
- Nondimensionalization wikiPageWikiLink List_of_dynamical_systems_and_differential_equations_topics.
- Nondimensionalization wikiPageWikiLink List_of_partial_differential_equation_topics.
- Nondimensionalization wikiPageWikiLink Logistic_map.
- Nondimensionalization wikiPageWikiLink Measurement.
- Nondimensionalization wikiPageWikiLink Measuring_instrument.
- Nondimensionalization wikiPageWikiLink Natural_units.
- Nondimensionalization wikiPageWikiLink Normalization_(statistics).
- Nondimensionalization wikiPageWikiLink Parametric_equation.
- Nondimensionalization wikiPageWikiLink Pendulum.
- Nondimensionalization wikiPageWikiLink Physical_quantity.
- Nondimensionalization wikiPageWikiLink Power_supply.
- Nondimensionalization wikiPageWikiLink Quantum_harmonic_oscillator.
- Nondimensionalization wikiPageWikiLink Quantum_state.
- Nondimensionalization wikiPageWikiLink RC_circuit.
- Nondimensionalization wikiPageWikiLink RLC_circuit.
- Nondimensionalization wikiPageWikiLink RL_circuit.
- Nondimensionalization wikiPageWikiLink Real_number.
- Nondimensionalization wikiPageWikiLink Resonance.
- Nondimensionalization wikiPageWikiLink Schrödinger_equation.
- Nondimensionalization wikiPageWikiLink Spectral_line.
- Nondimensionalization wikiPageWikiLink Standard_deviation.
- Nondimensionalization wikiPageWikiLink Standard_score.
- Nondimensionalization wikiPageWikiLink Statistical_dispersion.
- Nondimensionalization wikiPageWikiLink Statistics.
- Nondimensionalization wikiPageWikiLink Studentized_residual.
- Nondimensionalization wikiPageWikiLink Superposition_principle.
- Nondimensionalization wikiPageWikiLink Symbolic_computation.
- Nondimensionalization wikiPageWikiLink System.
- Nondimensionalization wikiPageWikiLink System_equivalence.
- Nondimensionalization wikiPageWikiLink Time_constant.
- Nondimensionalization wikiPageWikiLink Units_of_measurement.
- Nondimensionalization wikiPageWikiLink University_of_Bath.
- Nondimensionalization wikiPageWikiLink Variable_(mathematics).
- Nondimensionalization wikiPageWikiLink Wave_function.
- Nondimensionalization wikiPageWikiLink Wiktionary:intrinsic.
- Nondimensionalization wikiPageWikiLink Zero_of_a_function.
- Nondimensionalization wikiPageWikiLink File:Mass-Spring-Damper.png.
- Nondimensionalization wikiPageWikiLinkText "Nondimensionalization".
- Nondimensionalization wikiPageWikiLinkText "characteristic units".
- Nondimensionalization wikiPageWikiLinkText "elegantly simplify".
- Nondimensionalization wikiPageWikiLinkText "non-dimensionalised".
- Nondimensionalization wikiPageWikiLinkText "nondimensional form".
- Nondimensionalization wikiPageWikiLinkText "nondimensional".
- Nondimensionalization wikiPageWikiLinkText "nondimensionalised".
- Nondimensionalization wikiPageWikiLinkText "nondimensionalization".
- Nondimensionalization wikiPageWikiLinkText "nondimensionalize".
- Nondimensionalization wikiPageWikiLinkText "nondimensionalized".
- Nondimensionalization wikiPageWikiLinkText "scale".
- Nondimensionalization wikiPageWikiLinkText "scaled".
- Nondimensionalization wikiPageUsesTemplate Template:!.
- Nondimensionalization wikiPageUsesTemplate Template:Colbegin.
- Nondimensionalization wikiPageUsesTemplate Template:Colend.
- Nondimensionalization wikiPageUsesTemplate Template:Main.
- Nondimensionalization wikiPageUsesTemplate Template:Math.
- Nondimensionalization wikiPageUsesTemplate Template:Unreferenced.
- Nondimensionalization subject Category:Dimensional_analysis.
- Nondimensionalization hypernym Removal.
- Nondimensionalization type Company.
- Nondimensionalization comment "Nondimensionalization is the partial or full removal of units from an equation involving physical quantities by a suitable substitution of variables. This technique can simplify and parameterize problems where measured units are involved. It is closely related to dimensional analysis. 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.".
- Nondimensionalization label "Nondimensionalization".
- Nondimensionalization sameAs Q464133.
- Nondimensionalization sameAs Entdimensionalisierung.
- Nondimensionalization sameAs Adimensionnement.
- Nondimensionalization sameAs Redimensionalización.
- Nondimensionalization sameAs m.05n30h.
- Nondimensionalization sameAs Q464133.
- Nondimensionalization wasDerivedFrom Nondimensionalization?oldid=703614626.
- Nondimensionalization isPrimaryTopicOf Nondimensionalization.