Rotation in three dimensions | Theorems in geometry | Euclidean symmetries
In geometry, Euler's rotation theorem states that, in three-dimensional space, any displacement of a rigid body such that a point on the rigid body remains fixed, is equivalent to a single rotation about some axis that runs through the fixed point. It also means that the composition of two rotations is also a rotation. Therefore the set of rotations has a group structure, known as a rotation group. The theorem is named after Leonhard Euler, who proved it in 1775 by means of spherical geometry. The axis of rotation is known as an Euler axis, typically represented by a unit vector ê. Its product by the rotation angle is known as an axis-angle vector. The extension of the theorem to kinematics yields the concept of instant axis of rotation, a line of fixed points. In linear algebra terms, the theorem states that, in 3D space, any two Cartesian coordinate systems with a common origin are related by a rotation about some fixed axis. This also means that the product of two rotation matrices is again a rotation matrix and that for a non-identity rotation matrix one eigenvalue is 1 and the other two are both complex, or both equal to −1. The eigenvector corresponding to this eigenvalue is the axis of rotation connecting the two systems. (Wikipedia).
This video given Euler's identity, reviews how to derive Euler's formula using known power series, and then verifies Euler's identity with Euler's formula http://mathispower4u.com
From playlist Mathematics General Interest
Euler Angles and the Euler Rotation Sequence
In this video we discuss how Euler angles are used to define the relative orientation of one coordinate frame to another. Topics and Timestamps: 0:00 – Introduction and example 2:34 – The Euler Rotation Sequence 16:10 – Matlab animation showing rotation sequence 21:03 – The direction cos
From playlist Flight Mechanics
Euler's formulas, Rodrigues' formula
In this video I proof various generalizations of Euler's formula, including Rodrigues' formula and explain their 3 dimensional readings. Here's the text used in this video: https://gist.github.com/Nikolaj-K/eaaa80861d902a0bbdd7827036c48af5
From playlist Algebra
Linear Algebra 21g: Euler Angles and a Short Tribute to Leonhard Euler
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
Euler's Formula for the Quaternions
In this video, we will derive Euler's formula using a quaternion power, instead of a complex power, which will allow us to calculate quaternion exponentials such as e^(i+j+k). If you like quaternions, this is a pretty neat formula and a simple generalization of Euler's formula for complex
From playlist Math
Differential Equations | The solution of a Cauchy-Euler Differential Equation
We prove a general theorem regarding the form of a solution of a Cauchy-Euler Differential Equation. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Mathematics named after Leonhard Euler
How to derive Euler's formula using differential equations! Free ebook http://bookboon.com/en/introduction-to-complex-numbers-ebook A somewhat new proof for the famous formula of Euler. Here is the famous formula named after the mathematician Euler. It relates the exponential with cosin
From playlist Intro to Complex Numbers
Solves the Euler differential equation. Join me on Coursera: Matrix Algebra for Engineers: https://www.coursera.org/learn/matrix-algebra-engineers Differential Equations for Engineers: https://www.coursera.org/learn/differential-equations-engineers Vector Calculus for Engineers: htt
From playlist Differential Equations
Informal Proof of Euler's Formula (2 of 2: Trigonometric calculus)
If you enjoyed this, you can also check out my expanded series of videos that introduces Euler's Formula from "first principles" and concludes with Euler's Identity: https://www.youtube.com/playlist?list=PLHZZ0otaqNsWV01h2ZssT17Tj8fbtLiuM More resources available at www.misterwootube.com
From playlist Introduction to Complex Numbers
The second most beautiful equation and its surprising applications
Get free access to over 2500 documentaries on CuriosityStream: https://curiositystream.com/majorprep (use promo code "majorprep" at sign up) STEMerch Store: https://stemerch.com/ Support the Channel: https://www.patreon.com/zachstar PayPal(one time donation): https://www.paypal.me/ZachStar
From playlist Applied Math
The Math You Didn't Learn | #SoME2
Sometimes people wonder what actual mathematicians do. Do they crunch large numbers? Participate in competitions with each other? (They actually did a lot of that in the Middle Ages). Are they geniuses whose activites are unfathomable for us normal people? Math is a very large field, but m
From playlist Summer of Math Exposition 2 videos
YOU CAN'T USE EULER'S IDENTITY TO PROVE THE ANGLE SUM IDENTITIES! | Tricky Parts of Calculus, Ep. 4
I give multiple proofs of the angle sum identities sin(x+y) = sin(x)cos(y) + sin(y)cos(x) and cos(x+y) = cos(x)cos(y) - sin(x)sin(y) from different perspectives. I stress that a very common presentation of these formulas based on Euler's identity e^(ix) = cos(x) + i sin(x) is circular and
From playlist Math
Diego CORDOBA - Global smooth solutions for the inviscid SQG equations
In this lecture I will discuss some recent work, joint with Angel Castro and Javier Gomez-Serrano, on the existence of a non trivial family of classical global solutions of the inviscid surface quasi-geostrophic equation (SQG).
From playlist Trimestre "Ondes Non linéaires" - June Conference
Hausdorff School: Lecture by László Székelyhidi
Inauguration of the Hausdorff School The “Hausdorff School for Advanced Studies in Mathematics” is an innovative new program for postdocs by the Hausdorff Center. The official inauguration took place on October 20, 2015. Lecture by László Székelyhidi on "The h-principle in fluid mechanic
From playlist Inauguration of Hausdorff School 2015
Matt's Auction for Charity! =) http://ebay.us/RKeI74?cmpnId=5338273189 Epic Math Time: https://www.youtube.com/channel/UCisjF-Un7hf9lsMhoStF3OQ TheGermanFox: https://www.youtube.com/channel/UC7DT0FRbTpksPwpu520sz4g Xander Gouws: https://www.youtube.com/channel/UCzvvjULGBVuXZMN_yLS8OUQ Dil
From playlist Linear Algebra
Carla Farsi: Proper Lie Groupoids and their structures
Talk by Carla Farsi in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-Seminar.html on June 24, 2020.
From playlist Global Noncommutative Geometry Seminar (Americas)
Edriss Titi: Mathematical analysis of geophysical models
CONFERENCE Recorded during the meeting "Research School: Mathematical Advances in Geophysical Flows " the April 04, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathem
From playlist Jean-Morlet Chair - Hieber/Monniaux
Proving Euler's Formula (2 of 4: Differentiating both sides)
More resources available at www.misterwootube.com
From playlist Introduction to Complex Numbers
Remarks on the Long-Time Dynamics of 2D Euler by Theo Drivas
PROGRAM TURBULENCE: PROBLEMS AT THE INTERFACE OF MATHEMATICS AND PHYSICS ORGANIZERS Uriel Frisch (Observatoire de la Côte d'Azur and CNRS, France), Konstantin Khanin (University of Toronto, Canada) and Rahul Pandit (IISc, India) DATE & TIME 16 January 2023 to 27 January 2023 VENUE Ramanuj
From playlist Turbulence: Problems at the Interface of Mathematics and Physics 2023