In combinatorial mathematics, rotation systems (also called combinatorial embeddings or combinatorial maps) encode embeddings of graphs onto orientable surfaces by describing the circular ordering of a graph's edges around each vertex.A more formal definition of a rotation system involves pairs of permutations; such a pair is sufficient to determine a multigraph, a surface, and a 2-cell embedding of the multigraph onto the surface. Every rotation scheme defines a unique 2-cell embedding of a connected multigraph on a closed oriented surface (up to orientation-preserving topological equivalence). Conversely, any embedding of a connected multigraph G on an oriented closed surface defines a unique rotation system having G as its underlying multigraph. This fundamental equivalence between rotation systems and 2-cell-embeddings was first settled in a dual form by Lothar Heffter in the 1890s and extensively used by Ringel during the 1950s. Independently, Edmonds gave the primal form of the theorem and the details of his study have been popularized by Youngs. The generalization to multigraphs was presented by Gross and Alpert. Rotation systems are related to, but not the same as, the rotation maps used by Reingold et al. (2002) to define the zig-zag product of graphs. A rotation system specifies a circular ordering of the edges around each vertex, while a rotation map specifies a (non-circular) permutation of the edges at each vertex. In addition, rotation systems can be defined for any graph, while as Reingold et al. define them rotation maps are restricted to regular graphs. (Wikipedia).
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
Physics 11.1 Rigid Body Rotation (1 of 10) Basics
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the translational, rotational, and combined motion of rigid body rotation.
From playlist PHYSICS 11 ROTATIONAL MOTION
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
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
How to determine the rotation of a heart
👉 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
How does the fixed point affect our rotation
👉 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
3D Rotations in General: Rodrigues Rotation Formula and Quaternion Exponentials
In this video, we will discover how to rotate any vector through any axis by breaking up a vector into a parallel part and a perpendicular part. Then, we will use vector analysis (cross products and dot products) to derive the Rodrigues rotation formula and finish with a quaternion point o
From playlist Quaternions
24: Time change of vectors in rotating systems - Part 2
Jacob Linder: 16.02.2012, Matematikk 3 (TMA4345), v2012 NTNU A full textbook covering the material in the lectures in detail can be downloaded for free here: http://bookboon.com/en/introduction-to-lagrangian-hamiltonian-mechanics-ebook
From playlist NTNU: TFY 4345 - Classical Mechanics | CosmoLearning Physics
23: Time change of vectors in rotating systems
Jacob Linder: 16.02.2012, Classical mechanics (TFY4345), v2012 NTNU A full textbook covering the material in the lectures in detail can be downloaded for free here: http://bookboon.com/en/introduction-to-lagrangian-hamiltonian-mechanics-ebook
From playlist NTNU: TFY 4345 - Classical Mechanics | CosmoLearning Physics
Demonstrating Rotational Inertia (or Moment of Inertia)
Thank you to Arbor Scientific for letting me borrow their Rotational Inertia Demonstrator to … uh … demonstrate rotational inertia. Want Lecture Notes? https://www.flippingphysics.com/rotational-inertia-demo.html This is an AP Physics 1 Topic. 0:00 Intro 0:22 The Rotational Inertia Demons
From playlist AP Physics 1 - EVERYTHING!!
Merry-Go-Round - Conservation of Angular Momentum Problem
A 25 kg child is sitting on the edge of a #MerryGoRound. The merry-go-round has a mass of 255 kg and is rotating at 2.0 radians per second. The child crawls to the middle of the merry-go-round. What is the final angular speed of the merry-go-round? You may make the following estimations: T
From playlist AP Physics 1 - EVERYTHING!!
Spinning for stability by Ananyo Maitra
DISCUSSION MEETING : 7TH INDIAN STATISTICAL PHYSICS COMMUNITY MEETING ORGANIZERS : Ranjini Bandyopadhyay, Abhishek Dhar, Kavita Jain, Rahul Pandit, Sanjib Sabhapandit, Samriddhi Sankar Ray and Prerna Sharma DATE : 19 February 2020 to 21 February 2020 VENUE : Ramanujan Lecture Hall, ICTS
From playlist 7th Indian Statistical Physics Community Meeting 2020
Intermittent Planetary Mechanism
This mechanism produces a reciprocating movement, with the forward always longer than the backward. It uses a planetary mechanism with two inputs, the sun and the ring. The output is the arm. The inputs are provided by an intermittent mechanism, with one gear moving two others, one at a ti
From playlist Planetary Mechanisms
25: Rigid body motion - Part 1
Jacob Linder: 22.02.2012, Classical Mechanics (TFY4345), v2012 NTNU A full textbook covering the material in the lectures in detail can be downloaded for free here: http://bookboon.com/en/introduction-to-lagrangian-hamiltonian-mechanics-ebook
From playlist NTNU: TFY 4345 - Classical Mechanics | CosmoLearning Physics
Conservation of Angular Momentum Introduction and Demonstrations
Several demonstrations of #AngularMomentumConservation are shown using a rotating stool. The equations is also derived using Newton’s Second Law. Conservation of the direction of angular momentum is also demonstrated. Lecture Notes? https://www.flippingphysics.com/angular-momentum-conserva
From playlist AP Physics 1 - EVERYTHING!!
26: Rigid body motion - Part 2
Jacob Linder: 22.02.2012, Classical Mechanics (TFY4345), v2012 NTNU A full textbook covering the material in the lectures in detail can be downloaded for free here: http://bookboon.com/en/introduction-to-lagrangian-hamiltonian-mechanics-ebook
From playlist NTNU: TFY 4345 - Classical Mechanics | CosmoLearning Physics
Jörg Thuswaldner: S-adic sequences: a bridge between dynamics, arithmetic, and geometry
Abstract: Based on work done by Morse and Hedlund (1940) it was observed by Arnoux and Rauzy (1991) that the classical continued fraction algorithm provides a surprising link between arithmetic and diophantine properties of an irrational number αα, the rotation by αα on the torus 𝕋=ℝ/ℤT=R/
From playlist Dynamical Systems and Ordinary Differential Equations
Moment of Inertia Introduction and Rotational Kinetic Energy Derivation
The concept of kinetic energy applied to a stationary, rotating wheel is used to define Moment of Inertia and derive Rotational Kinetic Energy. Moment of Inertia is demonstrated. Want Lecture Notes? https://www.flippingphysics.com/moment-of-inertia.html This is an AP Physics 1 topic. 0:00
From playlist AP Physics 1 - EVERYTHING!!
How do the rotations of counter clockwise and clockwise similar
👉 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