Summing up, dimensional analysis is based on the homogeneity property of physical equations. Homogeneity is a further constraint on mathematical equations that is a necessary condition for correctness of physical equations. The fundamental result of dimensional analysis is the Buckingham pi theorem, which establishes the existence of dimensionless representation of physical equations. The dimensionless representation is useful in several ways, one of them is to establish dimensional similarity between systems.

Chapter Contents:

• 1.1 What is dimensional analysis?
• 1.2 What is dimensional similarity?
• 1.3 Application of dimensional analysis to science in general
• 1.3.1 Structure of physical relations
• 1.3.2 Dimensionless representation
• 1.3.3 Dimensional similarity
• 1.4 Application of dimensional analysis to control problems
• 1.4.1 Identification and model validation
• 1.4.2 Control theory
• 1.4.3 Control engineering
• 1.5 Book contents

Inspec keywords: mathematical analysis

Other keywords: Buckingham pi theorem; physical equations; mathematical equations; dimensionless representation; dimensional analysis; dimensional similarity; homogeneity property

Subjects: Mathematical analysis; Mathematical analysis; Mathematical analysis