Hamiltonian mechanics | Symplectic geometry
In mathematics and physics, a Hamiltonian vector field on a symplectic manifold is a vector field defined for any energy function or Hamiltonian. Named after the physicist and mathematician Sir William Rowan Hamilton, a Hamiltonian vector field is a geometric manifestation of Hamilton's equations in classical mechanics. The integral curves of a Hamiltonian vector field represent solutions to the equations of motion in the Hamiltonian form. The diffeomorphisms of a symplectic manifold arising from the flow of a Hamiltonian vector field are known as canonical transformations in physics and (Hamiltonian) symplectomorphisms in mathematics. Hamiltonian vector fields can be defined more generally on an arbitrary Poisson manifold. The Lie bracket of two Hamiltonian vector fields corresponding to functions f and g on the manifold is itself a Hamiltonian vector field, with the Hamiltonian given by thePoisson bracket of f and g. (Wikipedia).
11_7_1 Potential Function of a Vector Field Part 1
The gradient of a function is a vector. n-Dimensional space can be filled up with countless vectors as values as inserted into a gradient function. This is then referred to as a vector field. Some vector fields have potential functions. In this video we start to look at how to calculat
From playlist Advanced Calculus / Multivariable Calculus
Introduction to Vector Fields This video discusses, 1) The definition of a vector field. 2) Examples of vector fields including the gradient, and various velocity fields. 3) The definition of a conservative vector field. 4) The definition of a potential function. 5) Test for conservative
From playlist Calculus 3
Quantum Field Theory 5c - Classical Electrodynamics III
We end with a derivation of the classical interaction Hamiltonian for a charged particle moving in an electromagnetic field. There is a lot of "turn the crank" math in this installment, but the final result will be key to our continued development of quantum field theory.
From playlist Quantum Field Theory
Multivariable Calculus | Conservative vector fields.
We prove some results involving conservative vector fields and describe a strategy for finding a potential function. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Multivariable Calculus
Worldwide Calculus: Vector Fields
Lecture on 'Vector Fields' from 'Worldwide Multivariable Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Integration and Vector Fields
Calculus 3 Lecture 15.1: INTRODUCTION to Vector Fields (and what makes them Conservative)
Calculus 3 Lecture 15.1: INTRODUCTION to Vector Fields (and what makes them Conservative): What Vector Fields are, and what they look like. We discuss graphing Vector Fields in 2-D and 3-D and talk about what a Conservative Vector Field means.
From playlist Calculus 3 (Full Length Videos)
Multivariable Calculus | What is a vector field.
We introduce the notion of a vector field and give some graphical examples. We also define a conservative vector field with examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Multivariable Calculus
Physics - E&M: Ch 36.1 The Electric Field Understood (1 of 17) What is an Electric Field?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is an electric field. An electric field exerts a force on a charged place in the field, can be detected by placing a charged in the field and observing the effect on the charge. The stren
From playlist THE "WHAT IS" PLAYLIST
Calculus 3: Green's Theorem (8 of 21) Graphical Representation of a Vector Field
Visit http://ilectureonline.com for more math and science lectures! In this video I will show and explain a graphical representation of a conservative and NON-conservative vector field. Next video in the series can be seen at: https://youtu.be/7GpCErcgV4I
From playlist CALCULUS 3 CH 7 GREEN'S THEOREM
Brent Pym: Holomorphic Poisson structures - lecture 2
The notion of a Poisson manifold originated in mathematical physics, where it is used to describe the equations of motion of classical mechanical systems, but it is nowadays connected with many different parts of mathematics. A key feature of any Poisson manifold is that it carries a cano
From playlist Virtual Conference
18. Two State Systems (continued), Multiparticle States and Tensor Products
MIT 8.05 Quantum Physics II, Fall 2013 View the complete course: http://ocw.mit.edu/8-05F13 Instructor: Barton Zwiebach In this lecture, the professor continued to talk about nuclear magnetic resonance and also introduced the tensor product. License: Creative Commons BY-NC-SA More inform
From playlist 8.05 Quantum Physics II - Prof. Barton Zwiebach
MIT 8.422 Atomic and Optical Physics II, Spring 2013 View the complete course: http://ocw.mit.edu/8-422S13 Instructor: Wolfgang Ketterle In this lecture, the professor discussed QED Hamiltonian starting from electromagnetism. License: Creative Commons BY-NC-SA More information at http://
From playlist MIT 8.422 Atomic and Optical Physics II, Spring 2013
Symplectic Dynamics of Integrable Hamiltonian Systems - Alvaro Pelayo
Alvaro Pelayo Member, School of Mathematics April 4, 2011 I will start with a review the basic notions of Hamiltonian/symplectic vector field and of Hamiltonian/symplectic group action, and the classical structure theorems of Kostant, Atiyah, Guillemin-Sternberg and Delzant on Hamiltonian
From playlist Mathematics
Contacting the Moon - Urs Frauenfelder
Urs Frauenfelder Seoul National University January 19, 2011 GEOMETRY/DYNAMICAL SYSTEMS The restricted 3-body problem has an intriguing dynamics. A deep observation of Jacobi is that in rotating coordinates the problem admits an integral. In joint work with P. Albers, G. Paternain and O. v
From playlist Mathematics
How to Find Periodic Orbits and Exotic Symplectic Manifolds - Mark McLean
Mark McLean Massachusetts Institute of Technology; Member, School of Mathematics October 15, 2012 I will give an introduction to symplectic geometry and Hamiltonian systems and then introduce an invariant called symplectic cohomology. This has many applications in symplectic geometry and
From playlist Mathematics
Brent Pym: Holomorphic Poisson structures - lecture 1
CIRM VIRTUAL EVENT Recorded during the research school "Geometry and Dynamics of Foliations " the April 28, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on
From playlist Virtual Conference
16. Quantum Dynamics (continued) and Two State Systems
MIT 8.05 Quantum Physics II, Fall 2013 View the complete course: http://ocw.mit.edu/8-05F13 Instructor: Barton Zwiebach In this lecture, the professor talked about photon states, introduction of two state systems, spin precession in a magnetic field, general two-state system viewed as a s
From playlist 8.05 Quantum Physics II - Prof. Barton Zwiebach
17. Two State Systems (continued)
MIT 8.05 Quantum Physics II, Fall 2013 View the complete course: http://ocw.mit.edu/8-05F13 Instructor: Barton Zwiebach In this lecture, the professor talked about the ammonia molecule as a two-state system, ammonia molecule in an electric field, nuclear magnetic resonance, etc. License:
From playlist 8.05 Quantum Physics II - Prof. Barton Zwiebach
Lecture 9 | Quantum Entanglements, Part 1 (Stanford)
Lecture 9 of Leonard Susskind's course concentrating on Quantum Entanglements (Part 1, Fall 2006). Recorded November 27, 2006 at Stanford University. This Stanford Continuing Studies course is the first of a three-quarter sequence of classes exploring the "quantum entanglements" in mode
From playlist Course | Quantum Entanglements: Part 1 (Fall 2006)
Intro to VECTOR FIELDS // Sketching by hand & with computers
Vector Fields are extremely important in math, physics, engineering, and many other fields. Gravitational fields, electric fields, magnetic fields, velocity fields, these are all examples of vector fields. In this video we will define the concept of a vector field, talk about some basic te