Manifolds | Geodesic (mathematics)
In Riemannian geometry, the geodesic curvature of a curve measures how far the curve is from being a geodesic. For example, for 1D curves on a 2D surface embedded in 3D space, it is the curvature of the curve projected onto the surface's tangent plane. More generally, in a given manifold , the geodesic curvature is just the usual curvature of (see below). However, when the curve is restricted to lie on a submanifold of (e.g. for curves on surfaces), geodesic curvature refers to the curvature of in and it is different in general from the curvature of in the ambient manifold . The (ambient) curvature of depends on two factors: the curvature of the submanifold in the direction of (the normal curvature ), which depends only on the direction of the curve, and the curvature of seen in (the geodesic curvature ), which is a second order quantity. The relation between these is . In particular geodesics on have zero geodesic curvature (they are "straight"), so that , which explains why they appear to be curved in ambient space whenever the submanifold is. (Wikipedia).
Sometimes The Shortest Distance Between Two Points is NOT a Straight Line: GEODESICS by Parth G
What happens when the shortest distance between two points is NOT a straight line, and exactly what is a geodesic? Hey everyone, in this video we'll be looking at how the surface we happen to be studying impacts the definition of the "shortest" distance between two points on that surface.
From playlist Relativity by Parth G
Physics - Mechanics: Gravity (15 of 20) What is Geosynchronous Orbit?
Visit http://ilectureonline.com for more math and science lectures! In this video I will show you how to calculate the height for a satellite at geosynchronous orbit.
From playlist PHYSICS 18 GRAVITY
Introducing the Concept of Congruence
From playlist GeoGebra Geometry
Gravitation (8 of 17) Geosynchronous and Geostationary Orbits
Explains the difference between geosynchronous and geostationary orbits. Shows how to calculate the height above the Earth's surface needed to achieve a geosynchronous orbit. A geosynchronous orbit is an orbit around the Earth for a satellite so that the orbital period of the satellite ma
From playlist Gravitation: Orbital Velocity, Orbital Period, Potential Energy, Kinetic Energy, Mass and Weight
Straight Lines in Curved Space explained and visualized. Useful for the four dimensional space-time of Einstein’s General Relativity. My Patreon page is at https://www.patreon.com/EugeneK
From playlist Physics
Curvature for the general paraboloid | Differential Geometry 28 | NJ Wildberger
Here we introduce a somewhat novel approach to the curvature of a surface. This follows the discussion in DiffGeom23, where we looked at a paraboloid as a function of the form 2z=ax^2+2bxy+cy^2. In this lecture we generalize the discussion to the important case of a paraboloid, which we
From playlist Differential Geometry
Parallel session 8 by Dave Constantine
Geometry Topology and Dynamics in Negative Curvature URL: https://www.icts.res.in/program/gtdnc DATES: Monday 02 Aug, 2010 - Saturday 07 Aug, 2010 VENUE : Raman Research Institute, Bangalore DESCRIPTION: This is An ICM Satellite Conference. The conference intends to bring together ma
From playlist Geometry Topology and Dynamics in Negative Curvature
GPDE Workshop - Synthetic formulations - Cedric Villani
Cedric Villani IAS/ENS-France February 23, 2009 For more videos, visit http://video.ias.edu
From playlist Mathematics
Ergodicity of the Weil-Petersson geodesic flow (Lecture - 03) by Keith Burns
Geometry, Groups and Dynamics (GGD) - 2017 DATE: 06 November 2017 to 24 November 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru The program focuses on geometry, dynamical systems and group actions. Topics are chosen to cover the modern aspects of these areas in which research has b
From playlist Geometry, Groups and Dynamics (GGD) - 2017
Lecture 20: Geodesics (Discrete Differential Geometry)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg
From playlist Discrete Differential Geometry - CMU 15-458/858
Plenary lecture 11 by Keith Burns
Geometry Topology and Dynamics in Negative Curvature URL: https://www.icts.res.in/program/gtdnc DATES: Monday 02 Aug, 2010 - Saturday 07 Aug, 2010 VENUE : Raman Research Institute, Bangalore DESCRIPTION: This is An ICM Satellite Conference. The conference intends to bring together ma
From playlist Geometry Topology and Dynamics in Negative Curvature
What are Geodesics? | Graph Theory
What are geodesics in graph theory? We'll define them and give some examples in today's video graph theory lesson! And apologies for my mispronunciation and misspelling in this video. Remember that the distance between two connected vertices is the length of a shortest path connecting th
From playlist Graph Theory
PUBLIC LECTURE: Ergodic behavior in Negative curvature by Patrick Eberlein
Geometry Topology and Dynamics in Negative Curvature URL: https://www.icts.res.in/program/gtdnc DATES: Monday 02 Aug, 2010 - Saturday 07 Aug, 2010 VENUE : Raman Research Institute, Bangalore DESCRIPTION: This is An ICM Satellite Conference. The conference intends to bring together ma
From playlist Geometry Topology and Dynamics in Negative Curvature
Entropies for negatively curved compact manifolds (Lecture 1) by Lin Shu
Probabilistic Methods in Negative Curvature ORGANIZERS: Riddhipratim Basu, Anish Ghosh and Mahan Mj DATE: 11 March 2019 to 22 March 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore The focal area of the program lies at the juncture of three areas: Probability theory of random wa
From playlist Probabilistic Methods in Negative Curvature - 2019
L2 curvature for surfaces in Riemannian manifolds - Ernst Kuwert
Workshop on Geometric Functionals: Analysis and Applications Topic: L2 curvature for surfaces in Riemannian manifolds Speaker: Ernst Kuwert Affiliation: University of Freiburg Date: March 7, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
What is General Relativity? Lesson 44: Geodesic Deviation Part I
What is General Relativity? Lesson 44: Geodesic Deviation Part I A second way to understand the curvature tensor is by examining how nearby geodesics accelerate away from or towards each other. Please consider supporting this channel via Patreon: https://www.patreon.com/XYLYXYLYX and
From playlist What is General Relativity?
Curvature for the general parabola | Differential Geometry 13 | NJ Wildberger
We now extend the discussion of curvature to a general parabola, not necessarily one of the form y=x^2. This involves first of all understanding that a parabola is defined projectively as a conic which is tangent to the line at infinity. We find the general projective 3x3 matrix for suc
From playlist Differential Geometry
Einstein's General Theory of Relativity | Lecture 6
Lecture 6 of Leonard Susskind's Modern Physics concentrating on General Relativity. Recorded October 27, 2008 at Stanford University. This Stanford Continuing Studies course is the fourth of a six-quarter sequence of classes exploring the essential theoretical foundations of modern phys
From playlist Lecture Collection | Modern Physics: Einstein's Theory