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What Is Coordinate System
This section provides an introduction of coordinate system, which is a mathematical model associated with a frame of reference that converts every location in the frame into set of numeric value or values. 2022-10-21, ∼190🔥, 0💬

Observables in Phase Space
This section describes observables in phase space in terms of the Poisson brackets. 2024-12-14, ∼189🔥, 0💬

Hamilton's Principle - Stationary Action
This section provides an introduction of Action, an integral of Lagrangian function of a given system between two time instances. 2022-11-30, ∼189🔥, 0💬

2-Dimensional Cartesian Coordinate System
This section provides an introduction of 2-dimensional Cartesian coordinate systems, which uses perpendicular projections on 2 perpendicular axes to describe any locations in the frame of reference. 2022-10-08, ∼189🔥, 0💬

The Relativity of Simultaneity
This chapter provides an introduction of the relativity of simultaneity in special relativity. Topics include the definition of the relativity of simultaneity; a thought experiment showing the relativity of simultaneity. 2022-10-14, ∼188🔥, 0💬

1 Frame of Reference with 2 Coordinate Systems
This section provides an example of a frame of reference associated with 2 coordinate systems. The location of an object can be described as 2 sets of coordinates. 2022-10-18, ∼187🔥, 0💬

3-Dimensional Cartesian Coordinate System
This section provides an introduction of 3-dimensional Cartesian coordinate systems, which uses perpendicular projections on 3 perpendicular axes to describe any locations in the frame of reference. 2022-10-07, ∼187🔥, 0💬

Introduction of Special Relativity
This chapter provides an introduction of the special theory of relativity. Topics include 2 assumptions of special relativity; inertial frame of references; the principle of relativity; constancy of speed of light. 2022-10-08, ∼185🔥, 0💬

Poisson Bracket Expression
This chapter provides an introduction of phase space and phase portrait. Topics include Poisson Bracket as a partial differential expression; Hamilton Equations in Poisson Brackets; total time derivative of observables. 2024-12-14, ∼184🔥, 0💬

Poisson Bracket and Hamilton Equations
This section describes Hamilton Equations in terms of the Poisson brackets. 2024-12-14, ∼183🔥, 0💬

What Is Lagrange Equation
This section describes the Lagrange Equation states that the time derivative of the partial derivative Lagrangian against velocity equals to the partial derivative Lagrangian against position. A proof is provided to show that the Lagrange Equation is equivalent to the Hamilton Principle. 2022-11-11, ∼183🔥, 0💬

What Is Hamiltonian
This section provides a quick introduction to the Hamiltonian, which is a derived property of a mechanical system defined as the total energy, the sum of kinetic energy and potential energy of the system. 2022-10-08, ∼183🔥, 0💬

Frame of Reference with 2 Objects
This section provides an example of a frame of reference with 2 objects, where locations of other objects are described based where they are located on the line that connects the 2 reference objects. 2022-10-11, ∼181🔥, 0💬

What Is Frame of Reference
This section provides a quick introduction of frame of reference, which is a given object or objects we use as a reference to describe locations of other objects in the space. 2022-10-23, ∼180🔥, 0💬

Lagrange Equation on Simple Harmonic Motion
This section provides a quick introduction to the Hamiltonian function, the total energy of the system, which is the sum of kinetic energy and potential energy of the system. 2022-11-06, ∼179🔥, 0💬

Poisson Bracket in Portrait Space Transformation
This section describes observables in phase space in terms of the Poisson brackets. 2024-12-14, ∼178🔥, 0💬

List of Various Distances and Lengths
This section lists various distances and lengths to give us a sense of scale about space. 2022-11-05, ∼177🔥, 0💬

Other Proofs of the Lagrange Equation
This section provides two other proofs to show that the Lagrange Equation is equivalent to the Hamilton Principle. 2022-10-21, ∼177🔥, 0💬

Hamilton Equations in Cartesian Coordinates
This section provides a quick introduction to the Hamilton Equations in Cartesian Coordinates, partial derivative equations on the Hamiltonian function against position r and momentum p for an isolated conservative system. 2022-11-20, ∼176🔥, 0💬

Introduction of Speed
This chapter provides an introduction of speed. Topics include definition of speed; dependency of speed on frame of reference; measuring speed of light. 2022-10-04, ∼175🔥, 0💬

The Principle of Relativity
This section provides an example of law of physics, Newton's First Law of Motion, to help understanding the first assumption of the special theory of relativity: The Principle of Relativity. 2022-10-19, ∼173🔥, 0💬

What Is Poisson Bracket
This section provides a quick introduction to Poisson Bracket, which is an operation of two functions on the phase space (q,p) of a system. 2024-12-14, ∼172🔥, 0💬

What Is Time
This section provides a quick introduction of time, which is a property of our universe that gives us a sense of age of living things and speed of changing object. 2022-10-13, ∼170🔥, 0💬

Introduction of Lagrangian
This chapter provides an introduction of Lagrangian Mechanics. Topics include introduction of Lagrangian; Action, Hamilton Principle, Stationary Action, Lagrange Equations, examples of free fall motion; simple harmonic motion, simple pendulum motion. 2022-10-20, ∼169🔥, 0💬

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Android ASP Astrology Big5 Bitcoin Blowfish Built-in C# Calendar CD-DVD Cheminformatics Chinese Cryptography DES Email Encoding Ethereum Flash GB2312 General H Herong History HTML Java JavaScript JDBC JSP JVM Linux Molecule Movie Music MySQL Neural Network Perl PHP Physics PKI Publication Python REST SOAP Sorting Swing TV Series UML Unicode VBScript Web Web-Services Windows WSDL XML XMLPad XSD XSL-FO