CE507 Lecture 2 Coordinate TransformationStart with a coordinate system 123(,,)x xxa right-hand system with origin O. Rotate it to a new coordinate system, 123(,,)x xx′′′with the same origin O. Let , , 123ˆ ˆˆe e ebe the unit vectors along the123,,xxx−−−axes, and , , 123ˆ ˆˆe e e′′′the corresponding unit vectors along the 123,,xxx′′′−−−axes. Define: angle between the - (new) axis and - (old)axis.ijijxxα′=and ija= cos (ijα) = ˆˆijee′⋅, called the direction cosines. We will study the matrix [ ]()ijaa=in this lecture. Note that a given vector, x±, say, can have two different representations w.r.t. the two coordinate systems.
This preview has intentionally blurred sections.
Sign up to view the full version.