Rotation in three dimensions | Orientation (geometry) | Rotation | Euclidean symmetries
In geometry, various formalisms exist to express a rotation in three dimensions as a mathematical transformation. In physics, this concept is applied to classical mechanics where rotational (or angular) kinematics is the science of quantitative description of a purely rotational motion. The orientation of an object at a given instant is described with the same tools, as it is defined as an imaginary rotation from a reference placement in space, rather than an actually observed rotation from a previous placement in space. According to Euler's rotation theorem the rotation of a rigid body (or three-dimensional coordinate system with the fixed origin) is described by a single rotation about some axis. Such a rotation may be uniquely described by a minimum of three real parameters. However, for various reasons, there are several ways to represent it. Many of these representations use more than the necessary minimum of three parameters, although each of them still has only three degrees of freedom. An example where rotation representation is used is in computer vision, where an automated observer needs to track a target. Consider a rigid body, with three orthogonal unit vectors fixed to its body (representing the three axes of the object's local coordinate system). The basic problem is to specify the orientation of these three unit vectors, and hence the rigid body, with respect to the observer's coordinate system, regarded as a reference placement in space. (Wikipedia).
Describing rotation in 3d with a vector
Learn how a three-dimensional vector can be used to describe three-dimensional rotation. This is important for understanding three-dimensional curl.
From playlist Multivariable calculus
The rotation problem and Hamilton's discovery of quaternions IV | Famous Math Problems 13d
We show how to practically implement the use of quaternions to describe the algebra of rotations of three dimensional space. The key idea is to use the notion of half-turn [or half-slope--I have changed terminology since this video was made!] instead of angle: this is well suited to connec
From playlist Famous Math Problems
The virgin rotation matrix vs. the Chad axis–angle
In this video I talk about a lot of the representations for rotations in two and three dimensions. This is also really a Lie-algebra/Lie-group motivation video. Here's the text used: https://gist.github.com/Nikolaj-K/907e0ea3cc958c483572950b746e0145 Here's relevant links: https://en.wikip
From playlist Algebra
Linear Algebra: Rotation Transformations
Learn the basics of Linear Algebra with this series from the Worldwide Center of Mathematics. Find more math tutoring and lecture videos on our channel or at http://centerofmath.org/
From playlist Basics: Linear Algebra
Quaternions as 4x4 Matrices - Connections to Linear Algebra
In math, it's usually possible to view an object or concept from many different (but equivalent) angles. In this video, we will see that the quaternions may be viewed as 4x4 real-valued matrices of a special form. What is interesting here is that if you know how to multiply matrices, you a
From playlist Quaternions
Geometry: Ch 3 - Names & Symbols (1 of 8) Angles (Part 1)
Visit http://ilectureonline.com for more math and science lectures! In this video I will define the names and symbols used in naming angles in geometry, Part 1. Next video in this series can be seen at: https://youtu.be/sQSplye42-Q
From playlist GEOMETRY 3 - NAMES & SYMBOLS
R - Register Variation with Exploratory Factor Analysis
Lecturer: Dr. Erin M. Buchanan Summer 2019 https://www.patreon.com/statisticsofdoom This video is part of my human language modeling class. On our last video, we will cover exploratory factor analysis to capture the dimensional data that words can present. Note: these videos are part of
From playlist Human Language (ANLY 540)
Linear Algebra 21h: The Matrix that Represents an Arbitrary Rotation in 3D
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 3 Linear Algebra: Linear Transformations
[Lesson 13] QED Prerequisites - The Pauli Spin Matrices...from scratch!
The purpose of this video is to motivate the Pauli Spin matrices from first principles. We will use these matrices a lot during the study of QED and it is critical that every aspect of their design and origin is well understood. This video begins by describing what it means to "rotate a sp
From playlist QED- Prerequisite Topics
2020 Theory Winter School: Sung-Sik Lee
Topic: Field theories for non-Fermi liquids For more information on the 2020 Theory Winter School: https://nationalmaglab.org/news-events/events/for-scientists/winter-theory-school
From playlist 2020 Theory Winter School
R & Python - Exploratory Factor Analysis
Lecturer: Dr. Erin M. Buchanan Summer 2020 https://www.patreon.com/statisticsofdoom This video is part of my human language modeling class - this video set covers the updated version with both R and Python. Expanding on cluster analysis, this video examines how to put together concepts
From playlist Human Language (ANLY 540)
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
Progress and Prospects of Lattice Supersymmetry by David Schaich
PROGRAM Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography (ONLINE) ORGANIZERS: David Berenstein (UCSB), Simon Catterall (Syracuse University), Masanori Hanada (University of Surrey), Anosh Joseph (IISER, Mohali), Jun Nishimura (KEK Japan), David Sc
From playlist Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography (Online)
Linear Algebra 21i: How to Represent a Rotation with respect to an Arbitrary Axis
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 3 Linear Algebra: Linear Transformations
Some questions around quasi-periodic dynamics – Bassam Fayad & Raphaël Krikorian – ICM2018
Dynamical Systems and Ordinary Differential Equations Invited Lecture 9.2 Some questions around quasi-periodic dynamics Bassam Fayad & Raphaël Krikorian Abstract: We propose in these notes a list of some old and new questions related to quasi-periodic dynamics. A main aspect of quasi-per
From playlist Dynamical Systems and ODE
Topology in statistical physics - 4 by Subhro Bhattacharjee
PROGRAM BANGALORE SCHOOL ON STATISTICAL PHYSICS - XI (ONLINE) ORGANIZERS: Abhishek Dhar and Sanjib Sabhapandit DATE: 29 June 2020 to 10 July 2020 VENUE: Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the school will be conducted through o
From playlist Bangalore School on Statistical Physics - XI (Online)
Spinors and the Clutching Construction
What’s the connection between spinors and the clutching construction? Chapters: 00:00 Why should we care? 00:32 Spinors in pop culture 01:34 Graph 03:15 Wall 03:42 Tome 04:18 Sir Roger Penrose 04:53 Hopf fibration 06:23 Paul Dirac 07:12 The belt trick 08:54 Exterior derivative 09:49 Deter
From playlist Summer of Math Exposition Youtube Videos
ʕ•ᴥ•ʔ Simple Example of Geometry Transformations Rotations
Quickly master rotation symmetry and transformation. Watch more lessons like this and try our practice at https://www.studypug.com/geometry/transformations/rotational-symmetry-and-transformations When an object is turned around its center of rotation to certain degrees and the object loo
From playlist Grade 9 Math (Canada)
Looking at Euler flows through a contact mirror: Universality, Turing… - Eva Miranda
Workshop on the h-principle and beyond Topic: Looking at Euler flows through a contact mirror: Universality, Turing completeness and undecidability Speaker: Eva Miranda Affiliation: Universitat Politècnica de Catalunya Date: November 1, 2021 The dynamics of an inviscid and incompressible
From playlist Mathematics