Transforms | Hamiltonian mechanics
In Hamiltonian mechanics, a canonical transformation is a change of canonical coordinates (q, p, t) → (Q, P, t) that preserves the form of Hamilton's equations. This is sometimes known as form invariance. It need not preserve the form of the Hamiltonian itself. Canonical transformations are useful in their own right, and also form the basis for the Hamilton–Jacobi equations (a useful method for calculating conserved quantities) and Liouville's theorem (itself the basis for classical statistical mechanics). Since Lagrangian mechanics is based on generalized coordinates, transformations of the coordinates q → Q do not affect the form of Lagrange's equations and, hence, do not affect the form of Hamilton's equations if we simultaneously change the momentum by a Legendre transformation into Therefore, coordinate transformations (also called point transformations) are a type of canonical transformation. However, the class of canonical transformations is much broader, since the old generalized coordinates, momenta and even time may be combined to form the new generalized coordinates and momenta. Canonical transformations that do not include the time explicitly are called restricted canonical transformations (many textbooks consider only this type). For clarity, we restrict the presentation here to calculus and classical mechanics. Readers familiar with more advanced mathematics such as cotangent bundles, exterior derivatives and symplectic manifolds should read the related symplectomorphism article. (Canonical transformations are a special case of a symplectomorphism.) However, a brief introduction to the modern mathematical description is included at the end of this article. (Wikipedia).
Showing something is a linear transformation Check out my Linear Equations playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmD_u31hoZ1D335sSKMvVQ90 Subscribe to my channel: https://www.youtube.com/channel/UCoOjTxz-u5zU0W38zMkQIFw
From playlist Linear Transformations
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This video explains 2 ways to graph a linear transformation of a unit square on the coordinate plane.
From playlist Matrix (Linear) Transformations
In this video, I define a cool operation called the symmetrization, which turns any matrix into a symmetric matrix. Along the way, I also explain how to show that an (abstract) linear transformation is one-to-one and onto. Finally, I show how to decompose and matrix in a nice way, sort of
From playlist Linear Transformations
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In this video we discuss linear transformations. We start by examining the mathematical definition of a linear transformation and apply it to several examples including matrix multiplication and differentiation. We then see how linear transformations relate to linear systems (AKA linear
From playlist Linear Algebra
Math 060 102317 Matrix Representations of Linear Transformations III
Review of the construction of the matrix representation of a linear transformation with respect to bases. Review: matrix representation of a linear transformation between Euclidean spaces with respect to bases (not necessarily the standard bases). Example.
From playlist Course 4: Linear Algebra (Fall 2017)
Linear Algebra 15f: The Transformation of Translation
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
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Jacob Linder: 29.03.2012, 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
Jacob Linder: 11.04.2012, 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
Lecture 9 | Modern Physics: Classical Mechanics (Stanford)
Lecture 9 of Leonard Susskind's Modern Physics course concentrating on Classical Mechanics. Recorded December 20, 2007 at Stanford University. This Stanford Continuing Studies course is the first of a six-quarter sequence of classes exploring the essential theoretical foundations of mo
From playlist Course | Modern Physics: Classical Mechanics
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In this stream, we will look at how to incorporate more general "canonical transformations" into our Hamiltonian framework. Along the way, we will see some very deep relations between transformations, symmetries, and conservation, as well as some other interesting relations between paramet
From playlist Let's Learn (Classical) Physics: ZAP Physics Livestreams
44: EM field tensor and canonical transformations - Part 2
Jacob Linder: 28.03.2012, 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
45: Canonical transformations part 3
Jacob Linder: 29.03.2012, 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
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In this video we show how to transform a transfer function to an equivalent state space representation. We will derive various transformations such as controllable canonical form, modal canonical form, and controller canonical form. We will apply this to an example and show how to use Ma
From playlist Control Theory
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Jacob Linder: 12.04.2012, 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
Elmar Schrohe: Index theory for Fourier integral operators and Connes-Moscovici local index formulae
Talk by Elmar Schrohe in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on January 12, 2021
From playlist Global Noncommutative Geometry Seminar (Europe)
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From playlist Linear Algebra (Full Course)
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From playlist Workshop on Quantum Geometry