Rotation in three dimensions | Rotational symmetry | Orientation (geometry) | Geometric algebra
In geometry, a plane of rotation is an abstract object used to describe or visualize rotations in space. In three dimensions it is an alternative to the axis of rotation, but unlike the axis of rotation it can be used in other dimensions, such as two, four or more dimensions. Mathematically such planes can be described in a number of ways. They can be described in terms of planes and angles of rotation. They can be associated with bivectors from geometric algebra. They are related to the eigenvalues and eigenvectors of a rotation matrix. And in particular dimensions they are related to other algebraic and geometric properties, which can then be generalised to other dimensions. Planes of rotation are not used much in two and three dimensions, as in two dimensions there is only one plane so identifying the plane of rotation is trivial and rarely done, while in three dimensions the axis of rotation serves the same purpose and is the more established approach. The main use for them is in describing more complex rotations in higher dimensions, where they can be used to break down the rotations into simpler parts. This can be done using geometric algebra, with the planes of rotations associated with simple bivectors in the algebra. (Wikipedia).
Transformations on the Number Plane (2 of 2: Rotation & Reflection)
More resources available at www.misterwootube.com
From playlist Basic Linear Relationships
From playlist Two Dimensional Linear Transformations
7 Rotation of reference frames
Ever wondered how to derive the rotation matrix for rotating reference frames? In this lecture I show you how to calculate new vector coordinates when rotating a reference frame (Cartesian coordinate system). In addition I look at how easy it is to do using the IPython notebook and SymPy
From playlist Life Science Math: Vectors
What is the difference between rotating clockwise and counter clockwise
👉 Learn how to rotate a figure and different points about a fixed point. Most often that point or rotation will be the original but it is important to understand that it does not always have to be at the origin. When rotating it is also important to understand the direction that you will
From playlist Transformations
Exploring rotations in the coordinate plane with #Desmos. https://teacher.desmos.com/activitybuilder/custom/5f8cebfebc630a2d02e6560f #ImproveMyAB #geometry #RemoteLearning
From playlist Desmos Activities, Illustrations, and How-To's
Exploring 90 Degree Rotations in the Coordinate Plane
Exploring 90 degree rotations about ANY POINT in the coordinate plane: Conceptual investigation for students. https://www.geogebra.org/m/kbjdfg9r #GeoGebra #geometry #algebra
From playlist Geometry: Dynamic Interactives!
Calculus 3: Vector Calculus: Motion in a Plane (1 of 15) General Concept
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the general concept of motion in a plane (2-D) in vector calculus in relationship to position vector (r(t)), velocity vector (v(t)), and, later, acceleration vector (a(t)). Next video in the
From playlist CALCULUS 3 CH 3.1 VECTOR CALCULUS: MOTION IN A PLANE
Determining clockwise vs counter clockwise rotations
👉 Learn how to rotate a figure and different points about a fixed point. Most often that point or rotation will be the original but it is important to understand that it does not always have to be at the origin. When rotating it is also important to understand the direction that you will
From playlist Transformations
Geometric Algebra - 3D Rotations and Rotors
In this video, we employ the fact that two reflections is a rotation to perform rotations in 3D. We also will derive the general rotation formula, show how to compose rotations, and introduce the rotor version of this formula and discover the rotor's sign flip under a 2pi rotation. Refere
From playlist Math
Mod-01 Lec-2 Symmetry in Perfect Solids
Condensed Matter Physics by Prof. G. Rangarajan, Department of Physics, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in
From playlist NPTEL: Condensed Matter Physics - CosmoLearning.com Physics Course
Chemistry 107. Inorganic Chemistry. Lecture 02
UCI Chemistry: Inorganic Chemistry (Fall 2014) Lec 02. Inorganic Chemistry -- Symmetry and Point Groups View the complete course: http://ocw.uci.edu/courses/chem_107_inorganic_chemistry.html Instructor: Matthew D. Law License: Creative Commons CC-BY-SA Terms of Use: http://ocw.uci.edu/inf
From playlist Chem 107: Week 1
MIT 3.60 | Lec 4a: Symmetry, Structure, Tensor Properties of Materials
Part 1: 2D Symmetries View the complete course at: http://ocw.mit.edu/3-60F05 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 3.60 Symmetry, Structure & Tensor Properties of Material
Chemistry 107. Inorganic Chemistry. Lecture 01
UCI Chemistry: Inorganic Chemistry (Fall 2014) Lec 01. Inorganic Chemistry -- Course Introduction & Symmetry of Nature View the complete course: http://ocw.uci.edu/courses/chem_107_inorganic_chemistry.html Instructor: Matthew D. Law License: Creative Commons CC-BY-SA Terms of Use: http://
From playlist Chem 107: Week 1
Chemistry 107. Inorganic Chemistry. Lecture 03
UCI Chemistry: Inorganic Chemistry (Fall 2014) Lec 03. Inorganic Chemistry -- Representations and Character Tables View the complete course: http://ocw.uci.edu/courses/chem_107_inorganic_chemistry.html Instructor: Matthew D. Law License: Creative Commons CC-BY-SA Terms of Use: http://ocw.
From playlist Chem 107: Week 1
MIT 3.60 | Lec 11a: Symmetry, Structure, Tensor Properties of Materials
Part 1: Point Groups View the complete course at: http://ocw.mit.edu/3-60F05 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 3.60 Symmetry, Structure & Tensor Properties of Material
MIT 3.60 | Lec 8b: Symmetry, Structure, Tensor Properties of Materials
Part 2: Diffraction, 3D Symmetries View the complete course at: http://ocw.mit.edu/3-60F05 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 3.60 Symmetry, Structure & Tensor Properties of Material
QED Prerequisites Geometric Algebra 21 Rotors
In this lesson we introduce the notion of a "Rotor" which is a geometric product between two unit vectors. This critical notion will permeate all of our physics applications. Please consider supporting this channel on Patreon: https://www.patreon.com/XYLYXYLYX The software I usually use
From playlist QED- Prerequisite Topics
GAME2020 0. Steven De Keninck. Dual Quaternions Demystified
My GAME2020 talk on PGA as an algebra for the Euclidean group. Follow up on my SIGGRAPH 2019 talk : https://youtube.com/watch?v=tX4H_ctggYo More info on https://bivector.net
From playlist Bivector.net
Rotations in degrees for counter and clockwise directions
👉 Learn how to rotate a figure and different points about a fixed point. Most often that point or rotation will be the original but it is important to understand that it does not always have to be at the origin. When rotating it is also important to understand the direction that you will
From playlist Transformations