Electromagnetic Theory #6 Coordinate Transformations & Scale Factors скачать в хорошем качестве

Electromagnetic Theory #6 Coordinate Transformations & Scale Factors

In this lesson we bring together the three coordinate systems (Cartesian, cylindrical, spherical) and show how to convert unit vectors between them. We start with scale factors and a practical mnemonic for remembering them. Then we derive the transformation matrices from the general formula, introduce the transpose trick for inverse transformations, and work through examples — including cases where unit vectors from different coordinate systems appear in the same expression. Timestamps: 0:00 Intro 0:03 Recap & This Lesson 0:38 Scale Factors & Mnemonic 2:17 Transformation Formula & Cylindrical Matrix 3:53 Spherical Matrix & Transpose Trick 5:20 Worked Examples 7:05 Summary Topics covered: Scale factors h_ρ, h_φ, h_θ and how to remember them Mnemonic: new length coordinate = scale factor of new angle Right triangle relation: ρ = r sin θ General unit vector formula: ê_i = (1/h_i)(∂r/∂q_i) Cartesian ↔ Cylindrical transformation matrix derivation Cartesian ↔ Spherical transformation matrix derivation Inverse transformation = transpose (orthogonal matrices) Converting between cylindrical and spherical via Cartesian Example: ê_x + ê_y → cylindrical Example: ê_ρ + ê_θ → Cartesian (mixed coordinate systems) This video is part of the AcEdumy Electromagnetic Theory series. #ElectromagneticTheory #CoordinateTransformations #ScaleFactors #VectorCalculus #CylindricalCoordinates #SphericalCoordinates #Engineering #AcEdumy