Rigid Body transformation Lecture 1

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Presentation transcript:

Rigid Body transformation Lecture 1 Ruzena Bajcsy EE 125 Fall 2013

Outline Introduction to vector and matrix algebra Coordinates and Frames Rigid body transformations Properties of Rotation transformation. This is covered in the text Chapter 2, section 1. and 2.

Notation; v=column vector

Matrices

Operations on vectors; inner product is a scalar

Cross product is a vector

More on Matrices

Mechanics

Energy and Power

Coordinates and Frames

Rigid Body

Rigid Body motion

Rigid Displacement

Mathematical Representation of rigid displacement

Definition

Properties of vectors

Rigid Body Transformation

Examples of non-rigid transformation

Rigid motion as a change of coordinate frames

Rotation only

Examples of rotation matrices

Properties of rotation matrices

More properties of rotation matrices

Second property of rotation matrices

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